Freeciv aims to be mostly rule-compatible with Sid Meier's Civilization II, but a few rules are different which makes for a better multi-player game, and there are lots and lots ofadjustable parameters to make customizing games possible.
Although the graphics are not as good as those in Civilisation II, they are quite good, and there are many tiles sets available on the FreeCiv homepage. The rules are very complete, and the multiplayer and networking code is excellent. At the moment however, the game is lacking alliances, but FreeCiv is continually under development.
Note: FreeCiv requires an X windowing system, you can get one from StarNet, after 2 hours it times out though, so you'll need to purchase the full thing.