The way one ranks the Wonders of the World reflects on the type of game you play. These rankings more or less reflect the use that I have made of these of these wonders in my last two single-player games at Deity level, spaceship plus future tech mode.
1. Colussus: Foundation of the SSC; at the center of nexus of trade routes, improves science, wealth and happiness in other cities; while it eventually expires, you can get hell of a lot of mileage out of this wonder; in my opinion, by far the best of the ancient wonders.
2. Michaelangelo's Chapel: Essential for Deity level where the name of the game is controlling discontent.
3. King Richard's Crusade: Thanks to this wonder, I've built all of the subsequent Wonders in seven of the seven games. 'Nuf said.
4. Hoover Dam: increases industrial production while cutting industrial pollution; by far and away the most useful of the Modern Wonders.
5. United Nations: essential for the late game where you need to monitor the scientific progress of competing civs -- especially when they decide to pursue the Nuclear option; essential to prevent this being built by AI's, who can then exchange knowledge with all other civs; also helpful when waging war as a Democracy, especially if you know how to use your emissaries wisely.
6. Hanging Gardens: Combined with Michaelangelo's Chapel, quite effective at promoting "We Love the Consul/President's Day"; while it expires relatively early (w/ Railroad), at Deity level that one extra happy citizen in each city is often the one that triggers "We Love the Consul/President's Day," making this extremely useful for early demographic growth.
7. Cure for Cancer: by increasing happiness, has an indirect but essentially identical effect as Women's Suffrage when it comes to fighting wars as a democracy; by increasing happiness, promotes "We Love the President's Day," thus serving as replacement for the expired Hanging Gardens.
8. Shakespeare's Theatre: a sine qua non for waging war as a Democracy; requires careful thought as to its placement (ideally, an industrial port city that will be connected by rail with other major industrial cities).
9. Leonardo's Workshop: always nice to upgrade your units -- especially engineers! (The way I fight wars, this wonder seldom has had a significant military impact on my games.) However, it essential to keep this wonder out of a Computer Civ's control; I can imagine that in multiplayer games, this wonder becomes one of the most important, if not the most important wonder.
10. SETI: important for the late game where the competing civs are in alliance and essentially pursuing a common research program; and always good for the pursuit of future techs.
