Freeciv is a free Civilization-like game, primarily for X under Unix. It has support for multiplayer games locally or over a network, and an AI which gives most people a run for their money.
Freeciv aims to be mostly rule-compatible with Civilization II [tm], published by Sid Meier and Microprose [tm]. A few rules are different where we think it makes more sense, and we have lots and lots of adjustable parameters to make customizing games possible.
Freeciv has been implemented completely independently of Civilization; you do not need to own Civilization to play Freeciv.