Sid Meier's Civilization III/Wonders

The Colossus
The Colossus is one of the earlier Wonders, made available with the discovery of Bronze Working (a basic starting Advance), and rendered obsolete by "Flight". It is also one of the weaker Wonders, providing an extra point of commerce in every square of a city already producing at least one (meaning the Wonder is largely only good for already-large cities using many tiles).

Shakespeare's Theatre
Shakespeare's Theatre is a Wonder made possible by the "Free Artistry" Advance - the Advance that frequently gets ignored due to the presence of other, highly valuable Advances alongside it (such as Economics).

Depending on where you place the Wonder, the Theatre is either extremely good or pointless. It renders eight unhappy citizens content, which is superb for a massive city with perpetual happiness issues, but not so good for most other cities.

The Great Library
The Great Library is one of the most valuable Wonders of the early game. Made possible with the discovery of Literature, the Great Library automatically awards you any Advance known by two other civilizations. The value of this is readily apparent: if you are a civilization that's off to a slow start on Science, or is constrained by other reasons (such as the need to promote city happiness or deal with constant warfare), the Great Library acts as a great leveler.

The downside is that the "Education" Advance makes the Great Library obsolete, and that advance is only in the second tier of the Middle Ages, meaning that you only get to appreciate the Great Library for a short time.

Leonardo's Workshop
Halves the cost to upgrade a unit.

Smith's Trade Company
Smith's Trade Company is one of the most useful Wonders in the game. Made possibly by the discovery of the "Economics" Advance, it pays the entire cost for all commerce-related city improvements in your civilization (such as Banks, Marketplaces, Harbors, and so forth). If you are a prodigious builder, you usually find that this greatly increases your income over the course of a single turn.

It's an excellent Wonder for Democracy and Republic players, who are usually saddled with high unit costs.

Battlefield medicine
Allows units to heal in enemy territory, very important when one is on the offensive.
 * Presquite: build at least 10 hospitals.

Military Academy
Allows a civilization to build army (at a cost of 400 shields each), instead of merely grinding elite units to create a military leader.

The Pentagon
Allows four units to load into an army instead of just three. Requires three armies in the field.