I prefer to build wonders that permanently act as a city improvement in every city, as there are 33 city improvements to build (including 3 generations of barracks, and 4 types of power plant) which add up to a staggering 4720 shields, off course inland cities have less improvements, and things like power plants are mutually exclusive, and only one city can have the Palace. With a potential maintenance cost of about 83 gold, of course some of these improvements will generate income to offset this, and Adam Smith's Trading Co. can save up to 7 gold per turn. You can build wonders to permanently act as granaries, 2 generations of barracks (more or less), cathedrals, power plants, police stations, and research labs for all your cities. With a saving of 720 shields and 16 maintenance per city. The total cost of all the required wonders is 2700 shields, meaning you only require 3.75 cities worth of saved improvements to build them, a bargain!
The best wonder in the whole game is the Pyramids, a bargain at 200 shields (only 3 1/3 granaries). It effectively doubled population growth, saves 1 gold per city granaries, and reduces the chance of famine. It save 60 shields per city and removes an item from the build list in ALL cities, the savings can produce a phalanx and elephant, harbour, or two diplomats. Unlike granaries it is effective immediately a city is build, thus getting you colonies off to a flying start. At higher game levels computer opponents have faster city growth, so this offsets that advantage. If another power gets the Pyramids it will always build it in the capital, which will be protected by city walls by the time you can get at it, and unsubvertable, so begin granary construction immediately (with Adam Smith's Trading Company you will be freed of maintenance charges), occasionally capitals are moved, so then you can get it and subvert it. Sell any granaries you capture if you have the Pyramids to save maintenance costs, and get 60 gold.
Next go for the Hanging Gardens (200 shields) in the same city, this will mean you capital can maintain order up to level 8 with only a temple, and three resident units. Also all cities will be able to maintain order for one extra unit of population, giving new cities time to build units and temples. Be aware this wonder becomes obsolete when the railroad advance is discovered. Once your civilization gets quite big, disorder is increased by one per city, so you have to set the luxury rate to 20% or 30%, this will mean the city with the Hanging Gardens will probably get a 'We love the King' day, which approximately doubled trade output, you may need to build a few trade routes to trigger it. It Republic/Democracy it will mean +1 population per turn while food lasts, disorder (one unhappy person conceals it), Aqueduct (needed above 8) and Sewer System (needed about 12) permitting.
If you don't get the Hanging Gardens you must get the Oracle (300 shields). This is a good wonder, doubling the effect of Temples ie. 4 people content per temple, it does however become obsolete with the theology advance, so it is best to hold out for the monotheism advance and Michaelangelo's Chapel (400) which lasts for ever, and allows the powerful crusader unit.
If your lucky you might also be able to add the Colossus (200 shields) as well. You'll almost certainly have to demand tribute, request gifts, or sell improvements as by now other civilizations will have wonders well under way. It's a good wonder doubling trade/luxury/science arrow output in the city, but runs out when the flight advance is discovered, of course by then you will have a lot of trade from other cities so it doesn't make much difference, early on however it can speed up you science drive, or fatten you treasury. It's a good idea to build a marketplace and library in the city to maximise it's effect, they only costs 1 gold per turn each, and please you council of advisers when built in the capital.
The Lighthouse (200 shields) isn't worth bothering with. Although it allows triremes to navigate oceans without being lost, and increased ship movement by 1, not cumulative with Magellan, and it only lasts until the Magnetism advance. You triremes will have their work cut out mapping the coastlines which is most important. wait for the Navigation advance, and use the 200 shields to help build Magellan's expedition (400 shields) which increases ship movement by 2. The only exception is if you are behind on science and stuck on a continent with no other civilizations, then you need it to contact them and get back in the science race, but you might be too far behind to win anyway. Triremes are lost 50% of the time when not ending their turn next to land, only 25% when the Seafaring advance has been discovered, and 12.5% with the Navigation advance - still it's not worth the risk unless you're stuck on a continent.
Some people swear by the Great Wall (300 shields), I think it's a load of rubbish. It creates a few city wall in each city, double your units strength against barbarians, and forces civilizations at war to make peace with you. Unfortunately it only lasts until the metallurgy advance, then you are left high and dry with no city walls to defend your cities (units and population, remember there is no population lose in walled cities, and units have three times the defence rating, and they have no maintenance cost). Barbarians can be bribed by diplomats for relatively little money, these units can then be used to defend your cities allowing production to be used for something more useful then building units that will soon become outdated. There ships can also be taken sometimes before you have technology to build that type. One unit must be allowed to attack the city, so you can capture the leader for 150 gold, these making the whole enterprise virtually free, kill it if it's going to reek land improvement though. Always have a diplomat standing by, it's much more efficient and humane. The instant peace thing means, cities cost twice as much to bribe, as you have to subvert them when at peace, or your reputation will be damaged. Even at peace you can sometimes provoke a war by demanding tribute, this never works when you have the great wall.
The Great Library (300 shields) is a nice wonder to have but you can mange without it, there are usually better wonders to build - again some people swear by it but they are just lazy. Once built when a technology is trading or discovered, and at least two civilizations have it, you also get it, effects last until the electricity advance, so don't research electricity, magnetism or metallurgy (the two prerequisites) unless you have to, they're not much use any way - do however if a rival civilization has it, the civilization with cutting each science is either the largest or the one with the great library, god help if it is large AND had the library. If an ally has the library you can usually get the technology by requesting it as a gift, some allies aren't very friendly though like the French, Russians, Mongols and Zulus so won't - it's better not to Ally with them as demand tribute to maintain the Alliance, useful however if you army it weak, as war is impossible, giving you time to arm, they may end the alliance for no reason.
You can obtain all the technology you need by an early science drive 60% (despotism), 70% (monarchy) which will give you enough technologies to trade. Providing you have made a reasonably good job of exploration you should be in contact with at least three other civilizations. You can trade your technology A with one for their technology B, you can trade (if you are lucky) A and B on to another for C and D, then you can trade A, B, C, and D on to the final civilization for E, F, G, and H. Thus just with one technology A, you can get seven others for nothing. Of course it's now that easy, some civilizations are hostile and won't trade, other have most or all of the technologies you are offering, others are building a wonder using a technology you don't have, so won't trade until that wonder it build They usually build in several cities, so once one is complete they might go on to another wonder you don't know how to build, mean time they don't mind trading with other civilizations. This is a good reason to build as many wonders as possible.
You can allows use diplomats to steal from cities you are at war with, 30 shields a time, or subvert cities then you get to pick one technology. You must be careful what you trade, try to trade common technologies first, but civilizations usually want the best and latest ones, don't trade one for a wonder you're building if no one else has it until the wonder is build, or you have enough cash to build it if need be. You can also demand technology as tribute, but may start a war. When your power hits supreme however everybody suddenly hates you, and won't trade, this is when the library can be really handy, buy by this time it is almost obsolete anyway.
You must always be prepared for a science drive, try and have a library in every city it does help and it relatively cheap. You need to research the latest wonders sometimes so you get a head start in building them, and other useful technologies are Steam Engine (half a dozen Ironclads can bring any coastal city to it knees even if it has Musketeers, use them before Coastal Fortresses can be built, may have to research Physics first), Sanitation (to allow cities to grow beyond 12, you may need to research Medicine first), Explosives (effectively increases land improvement rates by 2.5 times), Machine Tools (for Artillery, build about 10 veteran ones are a rail link, and no city can stand against them, you may need to research Steel first).
Magellan's Expedition (400 shields) is a much better wonder to have than the Lighthouse, it adds two movement points to all your ships and never expires. I think it's stupid the way it can be built in inland cities, so always build it in a port, preferably next to a big ocean, not a lake or little sea. It makes exploration, colonization, and trade easier. It also increases the effectiveness of your navy by allowing then to outrun some ships, get to war zones quickly, or attack up to twice more per turn. Shore bombardments can be very effective when your enemy has city walls, but no coastal fortresses, but you must have Ironclads or better, and a good number of them. They trash classical units, and can be effective against musketeers, the technological window is quite small so act quickly, it's a good strategy for taking out enemy coastal capitals, then the remaining cities are a lot cheaper to subvert. Don't wait for ships to be built, buy them in your closest ports.
Sun Tzu's War Academy (300 shields) is in my option better than Leonardo's Workshop. If expires with the Mobile Warfare advance, ie. after two waves of barracks have become obsolete. You should focus your early research on getting this, its prerequisites are Monarchy (another very desirable advance) and Warrior Code (obtainable by trade from most Civilizations as it is an initial advance, and most AI Civilizations usually choose to research military technology). Wait until you have built a few of the early wonders before researching it, as once you get it, it will always be demanded in trades, so you want to be able to start building it straight away, so your technology trades aren't log jammed, without giving it away. Barracks are seldom useful except on the front-line of a war zone, anyway you will get some from captured cities, which can be connected to the front-line by railroad. The Academy means all units are created as Veteran, meaning even new cities can build good units - including vulnerable settlers (particularly useful for Island cities, where it would be difficult to ship units), and that surprise attacks by your enemies will be less successful. A lot of the units are closely balanced, so Veteran means you win most of the time, where with normal units you would lose most of the time. The Academy does not apply to ships. Also remember when upgrading units, you get half of the old unit build cost back again. New units can be shipped in from other cities, and the shields can be used to help build a wonder in the home city. The Academy will save you potentially 2 x 40 shields per Barracks per City, plus 1 gold maintenance for early barracks, and 2 for later barracks ie. A LOT!!!!
Marco Polo's Embassy (200 shields). This is a handy wonder, once built you get an embassy with every Civilization until Communism is discovered by someone. Be careful however and found proper embassies before it expires or you will be left blind at a critical stage of the game, when the rate of technology advance and wonder building is very fast. It's good for finding new civilizations after another one has been eliminated. I used to build this wonder all the time, but now don't bother as it makes the game too easy, it's much more fun discovering civilizations yourself, first you spot them, then contact them, and finally establish your embassy - sometimes you don't contact one till late and find it has developed into a powerful adversary. Diplomats cost 30 shields each, so if there are 7 civilizations you save 10 shields, plus the cost of ships, and a time delay. I think it would have been more realistic if the embassy was only established after you had located one of the civilizations cities. The United Nations has a similar effect, so build this to plug the gap later if you want.
King Richard's Crusade (300 shields), I used to think this wonder was a load of rubbish because it expired so soon, but I have changed my opinion. You probably won't have to research this as all Civilizations place a very high priority on discovering Invention for Leonardo's Workshop. Engineering is the prerequisite, and provides the Crusade. As soon as you get it begin construction as it doesn't last long, only until Industrialization ie. four steps Engineering -> Invention -> Steam Engine -> Railroad -> Industrialization, and the AI places a high priority on all these advances. If the AI gets Railroad it will build Darwin's Voyage and get Industrialization immediately, a particular problem if it is building wonders already, as the AI builds in several cities, so when one is built it switches to another. This is why you should build as many wonders as possible, so all are built, and the AI has to start from scratch. Build the Crusade in a high food city (double fish ones are particularly good with a harbour and granary if you don't have the Pyramids, as that is +4 extra food per turn which makes for fast population growth). Concentrate settlers on the city during building to open mines for faster production (also ship in caravans), after irrigate land and clear jungle/swamp for fast population growth, remember each unit of population equals an extra shield. Sea squares become very useful, needing no improvement and delivering 2 food, 2 trade, and a shield. You will be able to build an Aqueduct, Sewer System (if you have the technology), and Colosseum fast with the increased shield production, thus maintaining city growth. Once built, depending on terrain, you can get a new caravan every 2 or 3 turns (25 or 17 shields per turn, no other city can be this productive at this stage of the game), which means it can help build a lot of your other wonders quick, so basically you get this wonder for nothing, a bit like investing you money in a bank, and living of the interest. You may get a little pollution so have a settler near by to clean it up, as it may damage production.
Leonardo's Workshop (400 shields), expires with the Automobile advance. Personally (and I know A LOT of people will disagree with me) I think this wonder is over rated. Certainly it is a very useful wonder, but there are also many other useful wonders. The AI is geared to research Invention as soon as possible so it can get this wonder, so don't research any prerequisite technologies for Invention, you can get them is trades. What the Workshop does (in case you don't know - highly unlikely), is upgrade all old units with their latest versions, once you get the technology. Basically this wonder is just for lazy people who can't be bothered to upgrade their units, remember you get half the build cost of units back when you disband them. If an AI civilization gets this wonder it will have an advantage, but the AI is so stupid it won't make very good use of it, most of the games I play the AI only ever manages to capture a handful of cities, it's smarter when it uses WWII AI though, but then it has better weapons, industry, and can attack on land, sea and air. Be aware that upgrades only happen when you acquire new technology, so you might subvert units in the field or cities, which won't get upgraded straight away. If you do get the Workshop make sure you research Espionage, Tactics, and Explosives before anyone discovers the Automobile to get maximum effect. The trouble with this wonder, is that units created are non veteran, this leaves you open to surprise attacks. When upgrading a Veteran Phalanx to Pikemen for example, the defence rating goes DOWN from 3 to 2, against unmounted units. However, if you do have Sun Tzu's War Academy, if they win one battle they will always by upgraded. Make sure you have city walls and coastal fortresses to compensate for weakened defence, Artillery type units will also take much greater loses storming cities, as they usually only just win when veteran against many defence units.
This Wonder is very good for upgrading Settlers to Engineers (which work about 2.5 times as fast), but Settlers can be used to populate your smaller cities (up to level 8), or found new ones, which it is easy to neglect. If you don't colonize a site, you can be sure the AI will, and usually choose a poorer location, so even if you capture it, the city isn't as efficient as it could have been, or tactically useful (they seldom build port cities). Be aware that in some instances the Workshop won't upgrade units, e.g. you have a Caravel, and Discover Industrialization (prerequisite for a Transport), if you don't have the Magnetism advance (prerequisite for the Galleon) it won't get upgraded. Same applies to Horsemen -> Knights -> Dragoons.
Shakespeare's Theatre (300 shields), personally I never build this wonder. It is of limited value as it only applies to one city (use global happiness wonders they're much more efficient). It can be captured from another civilization anyway, with the bonus that the city won't suffer any disorder after capture as normally happens. Some people put this wonder in a high shield city near a war zone, which means that if they are a democracy or republic they can create a lot of units that won't cause disorder.
Copernicus's Observatory (300 Shields), this has to be one of the worst value wonders in the game, only giving you +50% Science in the home city. Wow we! You can get that with a library for 80 shields, and 1 gold maintenance per turn, 0 after you build Adam Smith's trading Company. Most civilizations will get the Astronomy advance early which allows this to be built, so you are not too likely to be able to build this one first anyway. Only build this if there is nothing better to build. It comes at the stage of technology where you should have researched enough technology to acquire all the new stuff by trade and espionage along, making it doubly useless. If you do decide to build it put it in the city that has the Colossus and Hanging Gardens (if you have them), as the +1 trade per square of the Colossus will be compounded by the +50% ie. x + 100% + x + 50% = +1.5x for two different cities, where as x + 100% + 50% = +2x. The Hanging Gardens will make 'We love the King' Day more likely, further compounding the advantage, or increase the population fast, which will increase the base x. You should also build a library and university in the city, for maximum effect. It is probably better though just to let another Civilization get it, and then let them research new technology faster, which you can gain through trade. Deity level is actually easier in this respect as your enemies get research bonuses meaning they get technologies quicker, which you can then get from them, allowing you to concentrate on trade and luxuries. This is why I sometimes play at King level, it is in some respects more difficult, as no one gets any bonuses ie. a level playing field, I also play at this level when playing a weak civilization in a scenario, or to stop the computer clogging the board up with cheap units that just slow the game down.
Isaac Newton's College (400), this adds +100% science to the home city. You need to discover Theory of Gravity (prerequisites Astronomy and University) to get it, not many civilizations research this, so if it comes up on your research list, shunt a bit of effort into researching it, and you will have it built before they even discover Gravity. This is why it is a good idea to build libraries in every city when you get a chance, they cost little or nothing to maintain, and greatly aid rush research, I never used to bother with them until very late, but have changed my mind. A good time to build them is just before Aqueducts ie. when your city reaches level 8, switch workers from food rich to shield rich squares (make sure you have improved some in readiness), also build city walls (free maintenance), and marketplaces (effectively free maintenance, as they effect trade AND luxuries, and you always have a bit of one or the other). Remember an Aqueduct costs 2 gold per turn, and you will also have to build happiness Wonders or improvements to maintain order in +8 cities. Same rules apply to the College as for Copernicus's Observatory, obviously build it in the same city. Total benefit will be x + 100% (for Colossus) + 75% (approx., for Hanging Gardens and 'We love the King Day' - of course this Wonder will run out soon after you build the College) + 50% (for Observatory) + 100% (for College) + 100% (for Library and College) = +20x!!! This means that one city may research as much as all your other cities combined, a bit like Oxford or Cambridge, small but highly effective. If you have to choose between putting it in the city with the Colossus or Observatory, choose the Observatory as the Colossus becomes obsolete, the Observatory last forever. It's a pity you can't set the science rate by city, so some cities can concentrate on commerce, others on industry, others on entertainment, others on producing settlers for new cities, and others on science, after all this happens in the real world.
Michaelangelo's Chapel (400 shields), this is a very useful wonder effectively giving you a cathedral in every city with zero maintenance. Particularly good for a fundamentalist governments as every city will provide between 2 and 4 gold per turn for nothing. Cathedrals cost 160 shields plus 3 gold maintenance and take a considerable time to build so this wonder is a bargain, it only costs 2.5 cathedrals. You need to start building it before everyone else as it is quite popular, so make sure you have polytheism (one prerequisite advance), then research philosophy, if you get it first, you get to pick a free advance, and hopefully you will be able to pick monotheism, thus giving yourself a flying start. If someone else gets philosophy first, try to acquire it from them, then research monotheism. Don't waste shields on the Oracle hold out for this wonder, increase the luxury rate or hire entertainers if you have to. Cathedrals keep a base 3 people happy per city, Theology adds 1 to this, Communism takes 1, so a cathedral can keep between 2 and 4 people happy depending on your technology. For this reason I don't like acquiring the Communism advance, particularly when I have the Statue of Liberty which allows you to switch to a Communist Government.
J.S. Bach's Cathedral (400 shields), this wonder keeps 2 unhappy people happy in every city. Particularly useful for Republican and Democratic governments. It allows an additional 2 units to be out of cities and frontier forts without causing disorder for the Republic, total 3, you get one free anyway. And 1 unit for Democracy. If the home city has a police station or you have the Women's Suffrage wonder, you can have as many units out in a Republic as you want, and 2 for a Democracy. Remember triremes, and caravels also cause disorder, so try to acquire technology to build galleons or transports, this makes trade and exploration easier and faster. This wonder also helps maintain general order, particularly for governments who can't depend on martial law. Remember the base level of disorder is increased by 1 for each game level, and if you have more than about a dozen cities.
The Eiffel Tower (300 shields), requires Steam Engine advance. You get this wonder at a period when there are a lot of other more useful wonders to build. It makes other civilizations less hostile to you, even if you have wronged them, the effect increases over time, but extremely slowly. You can get the decrease in hostility by capturing the Wonder as well, so if you had a really bad reputation, you could capture this wonder, lose it, capture it again etc... and end up with a spotless reputation, not very realistic. If you play dirty, this wonder is a lot more useful. But there are many ways to start wars with out damaging you reputation like paying one power to attack another, then there is a change the other powers spies will find out and declare war on you, with the added bonus that you have an ally in your war, pay the powers ally to break the alliance and then they won't declare war on you as well, as usually happens. Demand tribute (can't use this option for Republics and Democracies), and even on occasion withdraw troops works well, especially for strong aggressive powers, even if you are weaker you can usually out think the AI in a war. Once your power reaches supreme reputation doesn't matter as much as everyone hates you anyway and won't trade with you, unless an ally but then at a price. They are less likely to mount surprise attacks though, but you are strong so it doesn't matter that much any way. My advice is let someone else build this and then capture it (unless you reputation is very bad), you can even break a treaty to go to war, as once captured your reputation will be repaired. AI civilizations like to build this in their Capitals so it is more difficult to capture.
Adam Smith's Trading Company (400 shields), requires Economics (prerequisites Banking and University). You usually get this wonder when a lot of others are also available so you will have to decide how much you want it, you can of course also capture it. This is a very useful wonder paying the maintenance for all 1 gold improvements. These are temple, granary, marketplace, library, courthouse, harbour, coastal fortress, and ancient barracks (probably obsolete or about to become so). Once you get this wonder concentrate production on building the above improvements after wonder and military concerns. Once built population growth rate will be doubled or more (with harbours), trade/luxuries will be up 50%, science will be up 50%, shield/disorder/revenue corruption will be down 50%, and coastal defence will be doubled. If you have limited trade coming in it may not be worth it straight away, if you become a fundamentalist government there are effectively no shields used to maintain units so production is very fast, and the increased revenue from religious earning makes it a good time to build the marketplace, libraries won't be much use with this government type as they have -50% science, but you can prepare for when you change, also give any cities walls who don't have them, to increase defence and protect the population.
A lot of people underestimate the worth of granaries and harbours, they greatly speed the growth rate of cities, allow more settlers, which further increases it, making for strong cities soon, while your enemies are weaker. If you get to needing a Aqueduct or Sewer System and don't have the technology either build setters to found new colonies, or make some citizens scientists (+3 base science, particularly useful in cities with science wonders) or tax men (+2 base gold). I used to underestimate the use of courthouses, but they are very good at preventing disorder when switching governments, always build them once you get one shield corruption (this shield disappears as upkeep if you build a extra unit). Road, and Railroad links to the Capital reduce corruption, as does distance, so build cities close to the Capital. Courthouses also add 1 happy citizen for democracies. Only build Coastal Fortresses when enemy naval force starts appearing near your cities, or if it looks like war is about to break out, or if you have nothing better to build, making way for future improvement not yet discovered. They can reck a lot of ships.
The Statue of Liberty (400 shields), requires Democracy (prerequisites Invention and Banking). This allows you to switch to ANY government type (even if you haven't discovered the necessary advance) with only one turn of anarchy (sometimes anarchy can last a very long time). I used to think this was a good wonder, now I think it is a excellent wonder. However, not very realistic as I can hardly see the Americans switching from Democracy to Communism or Monarchy in one turn, perhaps it should only have worked when you switch to a more liberal type of government than the present one. Clearly your not going to want to change to Despotism, although you can. You usually get this wonder when a Monarchy, it a pity it doesn't ask you if you want a revolution as soon as it's built like when you acquire a new government advance, as I tend to forget and only realise about 20 turns later. As soon as it is built switch to either Communism or Fundamentalism.
Choose Communism if you are presently having a science drive, it has less corruption, up to 80% research, veterans spies, and 3 units can keep 6 unhappy citizens content. Otherwise choose Fundamentalism, this has -50% science so it no good for research, but has less corruption, 1 gold back for every citizen that is kept happy by improvements or wonders, up to 80% tax, and can support 10 units free per city! I used to think this government was rubbish but now quite like it. This government is very good for building as effectively all shields are used for building, none are wasted in corruption or unit maintainence. So while you are this government give all your cites the cheap maintainence improvements if they don't already have them ie. Temple, Granary, Harbour, City Walls, Coastal Fortress, Marketplace, Library, and Courthouse - you can also churn out of few diplomats, colonists, and military units. Some improvements might not be useful now but prepare you for when you switch government, or are faced with a large military build-up. As science is stalled make sure you have the Libraries so you can catch up when you switch. This type of government generates a lot of cash that can be used to subvert cities, allowing you to obtain new science though conquest, while weakening your enemies. You also aren't forced to sue for peace when it is not in your interest. Once the Fundamentalism advance is discovered cheap (20 shield) Fanatics can be built with a Defence/Offence rating of 4, I prefer Alpine Troops or Mech. Inf., they are more expensive, but also more reliable, and it is more humane to use them as less of them die. Settlers require two food for these types of government so watch out for starvation, also when you switch from Fundamentalism watch out in case some cities can't support all their units. Once you have Factories and Hydro Plants a Democracy can out produce Fundamentalism, their maintenance is to great a strain on Fundamentalism. AI Fundamentalist governments can be very dangerous with advanced technology, as they produce a phenomenal amount of units.
You don't have the demand tribute option as a Republic or Democracy, so this wonder allows you to switch for a turn and incite a war, then switch back to fight with a stronger government. You can actually try out all government types during the turn of switching. These types of governments have a lot of disorder problems so don't switch to them straight away. Use other government types to build Marketplaces and Courthouses which make you luxury spending more effective, also have some happiness wonders or improvements including Women's suffrage, and wait until you have galleons and transports as they have no attack factor so don't cause disorder. Once your cities reach 12+ it is probably a good time to switch. Also create some trade routes to increase the amount of luxuries reaching cities. I find you can get by with a 10% rate (not straight away though, sometimes you have to start a 30% or 40% and see to the worst effected cities before lowering), but 20% makes 'We love the President' days which are good for fast population growth. If you switch too early you will be crippled by a lack of shields, Democracy is so easy late in the game it is almost cheating. Republic makes fighting wars easier, with a 50% chance that you can override the senate, and less unit disorder problems.
Darwin's Voyage (400 shields), requires Railroad (prerequisites Steam Engine and Bridge Building - which you will almost certainly have by the time you acquire the Steam Engine). This Wonder gives you two free advances when built, so once you start building it don't spend any money on scientific research until it's completed, as every advance increases the cost of researching the next advance, and I think although am not sure that some or all of the built up research gets wiped out. You should get this Wonder not so much for the benefits it gives you, as for the benefits it deprives your enemy of. At this stage in the game several Wonders are already simultaneously in production. If an enemy builds this, they are almost certain to get Industrialization, and then either Communism straight away, or Genetic Engineering or Electronics very shortly. All these Wonders are very useful, and your enemy is highly likely to share the technology with other powers, meaning you will be over stretched and unable to build all the Wonders first. If you build the Voyage: they are more likely to cancel building as they have nothing else to build thus having to start from scratch; you don't have to divert money that could buy Wonders to Scientific Research; and you will have a head start.
Women's Suffrage (600 shields), requires Industrialization. This is a useful wonder for Republics or Democracies making units away from cities, or forts (with in 3 squares of a city) cause 1 less unhappiness. This means a republic can have any number of units in the field with out disorder, and a Democracy twice as many, if you build a Courthouse this makes a citizen happy, so one more unit can be let out. Remember you are allowed one unit out free in a Republic anyway. It is still a good idea to build forts for units even if they're not causing unhappiness as it doubles their defence, however the AI likes to subvert units in forts or mountains when at war, so either have two units together (the strongest unit always defends), become Democratic (unsubvertable units), or include a Diplomat (political officer like the Soviets used) to prevent defections, then you won't have to pay additional maintenance and can subvert enemy units if the battle is going badly. Even if you are not a Republic or Democracy, at some time you a likely to be, so build this wonder to be prepared, it makes switching to more free types of government easier. This wonder also saves you building Police Stations in every city at a cost of 60 shields and 2 gold per turn.
The United Nations (600 shields), requires Communism (everyone will have Philosophy by now so Industrialization is the only real prerequisite). Personally I never build this wonder, it prevents war breaking out (including stopped units violating your territory), establishes an embassy with every civilization (even ones you don't know about, but most will already be founded already), and gives you a 50% chance of over riding the Senate in negotiations (your reputation will still be damaged though if you break treaties, and the government can still fall). The trouble with this wonder is that it prevents you being able to provoke other civilizations into war, so you either have to damage your reputation or pay another power to declare war and hope that will provoke them. This wonder is only really useful if you are very weak (in which case you probably won't have the science and shields to build it), or play like a saint. The Communism advance also reduces the effectiveness of Cathedrals by 1.
The Hoover Dam (600 shields), requires Electronics (prerequisites Electricity and the Corporation). Acquire or research Electricity as it becomes available, this will increase your chances of getting Electronics first. Electricity also has the advantage of putting a enemies Great Library out of action, if you have the Library you probably don't want to research it, but don't be complacent, you only get advances after two other powers, so someone could begin constructing wonders before you. Electronics also makes Colosseums keep 4 people content instead of the previous 3, at the same cost, and by this time Cathedrals will be less effective due to Communism reducing their effect by 1, so build Colosseums first, where previously you would have built Cathedrals first, they costs less shields for the same cost per citizen. The Hoover Dam is a very powerful wonder, adding 50% to the shield output of Factories AND reducing city shield based pollution by 50%. It works for cities you own on any continent. I don't tend to build Factories until I have constructed this wonder, to prevent excessive pollution. I only build them in low shield cities with less than 10 shields per turn after unit maintenance (as a rule of thumb), unless there or hills that haven't been mined yet. Also recently conquered cities that have had virtually all improvements destroyed, just keep an Engineer near by to mop up pollution. It is best to buy Factories, they don't cost much, otherwise you will be waiting for ever, and will probably have to switch back to a population growth, or civic order improvement anyway before it's finished.
Discovering Industrialization adds 1 to base city pollution, that is why you don't really see any pollution before Industrialization. Each unit of population and shield causes 1 pollution times base pollution rate, but the first 20 are neglected. They represent the percentage chance of a square by the city getting polluted, so if you have 10 pollution, that's 10% chance per turn. Squares hit by pollution have production halved. Given enough pollution global warming will occur. If you don't get the Hoover Dam your enemy will be stronger, but Electronics allows Hydro Plants to be built in any city with a river or mountain next to it (I always build the Hoover Dam in this type of terrain, the game should limit wonders to appropriate terrain it would make it a little more challenging and interesting), but it costs 240 shields and 4 maintenance per turn, if the city has a power plant sell it as they are not cumulative, and power plants add 50% pollution, not take it.
The Cure for Cancer (600 shields), requires Genetic Engineering (prerequisites Medicine and the Corporation). Once Industrialization is discovered the Corporation follows soon after, this is a time when a number of expensive wonders will be in construction, Women's Suffrage, and soon after the United Nations, the Cure for Cancer and the Hoover Dam, both have the Corporation as a prerequisite. Cure for Cancer adds one happy citizen to each city, not cumulative with the Hanging Gardens as that has become obsolete, even if you change rules.txt it still isn't cumulative. This will make 'We love the President' days more likely especially if you have a 20% luxury rate and courthouse, this will mean you city population increases by 1 each turn food, aqueducts, and sewer system permitting, until 1 unhappy citizen appears, or less than 50% of the population are happy. This can double your population in a very short time, making you empire much more powerful, but also creating pollution problems, and meaning other powers will probably be more hostile to you. Genetic Engineering isn't the prerequisite for anything and doesn't allow any new units or city improvements to be built, so if the Cure for Cancer has been built it is pointless to research it.
The Apollo Program (600 shields), requires Space Flight advance (prerequisites Rocketry and Computers). Unless you a total dumb dumb you've probably won by now. This is one of the last wonders, and reveals all current cities on the map to everyone, and allows the construction of spacecraft. You should have the world well mapped already, with naval and freight units, of course a few cities may allude you, and their sizes, land improvements, and transport links may be way out of date. Don't build this wonder because someone else will and you will get all the benefits anyway, and you don't want to start the space race early. Use the time to increase your industrial muscle building Factories, Power Plants, Pollution Control and Manufacturing Plants, so you can build the best Space Ship in the Shortest time, and you'll have an additional 600 shields to build it with. Or you could build an army to wipe out you opponents before or while they're constructing the ship, if you capture their Capital their ship is destroyed. You will also need the Plastics and Superconductor advances to build the more complex elements of the ship, be aware the Plastics advance increase the base level of pollution for a city by 1. Space Ships can not be built if you selected the bloodlust option in customise game (even if you're winning!), this may also be set in some scenarios.
The SETI Program (600 shields), requires the Computers advance (prerequisites Miniaturization and Mass Production). This advance acts as a research lab in every city (you can't build the research lab as well of course), ie +50% science per city, with savings for every city of 3 gold per turn and 160 shields. To make sure you get the greatest chance of getting this wonder, make sure you acquire Miniaturization, as it is available long before Mass Production. Be aware discovering Mass Production increases the base level of pollution per city by 1. If you are able to research and build this wonder you don't really need it, as by this stage of the game virtually all research has been completed, and you are by definition number one in science. It is a good one to steal if you are way behind on research, especially as if you are behind you get research bonuses, reducing the time to discover each new advance. Another use for this wonder is in a post nuclear scenario, where most of your research tree has been wiped out, and you have to discover almost everything again. This advance could be renamed and made to appear a lot earlier by modifying rules.txt, then it would prove extremely powerful.
The Manhattan Project (600 shields), this is one of the last wonders to be built and only a fool would consider building it. It requires the Nuclear Fission advance to build. Once built any power with Nuclear Fission and Rocketry can build nuclear missiles (200 shields a piece), so there is no point wasting shields building it yourself, when someone else will anyway. Make sure you have the technology to build nuclear missiles before this is constructed or you WILL be open to nuclear blackmail, construct at least one missile immediately even if you never intend to use it. The AI's attitude chances depending on whether you have nucs or not, non nuclear powers are more compliant if you have them, but if you don't nuclear powers will demand tribute, pay up as the nuclear option combined with paratroops can be devastating. I never use nucs as they wipe out half a cities population, it garrison and units in the 8 surrounding squares (yours and anyone else's included, luckily this doesn't trigger a war, although it should), and trashes many improvements in the attack, and more when you occupy the city. Also it creates a lot of pollution that can soon lead to global warming which will cut the shield and trade output of your cities dramatically, and lead to starvation, pollution is also very difficult to clean up in a war zone. It is much better to subvert cities, or bribe one power into a war with another so both are weakened. This is one wonder the AI doesn't automatically build, if it does try subverting the city building it. Having nucs will make an attack less likely, if it does happen nuc their capital and occupy it, it might lead to civil war if your lucky and there is a free AI slot. Once a capital falls other cities are a lot cheaper to subvert, until a new one is built, so have spies standing by, the cost of subverting cities is 50% less using spies, less still if they are veteran, destroy the courthouse and it is halved again. Spies can plant nuclear bombs, but make sure you are at war or EVERY power will declare war on you if you are detected, unless you are a Fundamentalist government.