Title: Freeciv.
Developer: Various.
Version: 2.1.4.
Development Status: Full Version/Beta.
Requirements: Windows, Linux, Mac OS X, GTK+ (graphic library, freely available).
Rating: 8/10.
Site: http://www.freeciv.org/
Description: A clone of Civilization. Can be played single-player but is made more for multiplayer. Open source so it is continually being improved. Includes both a "client" and "server" component. You must start the "server" component first before you can run the "client" and join the game. You can also have other people join your "server" or you can join others "servers." I figured it out in maybe two or three minutes. For those mainly looking to play single-player, I'd probably recommend C-evo as a good alternative.
Features: AI, Multi-Player.
Screenshot: