The Civilization series has inspired several unofficial Civ-like games.

The most notable ones are probably C-evo, Freeciv, and FreeCol. The first two resemble Civilization II, while FreeCol is a remake of the original Sid Meier's Colonization.

Those three are all free to download and play, and there are some options for two or more human players to compete. There is no sign that the developers plan to stop making improvements.

The term "unofficial" should probably include the commercial game Call to Power II, because it was produced without any license from any company associated with Sid Meier after the producer had had a license to produce one game using the name; that was Civilization: Call to Power.

Civilization Series

Official series:
Civilization II + Conflicts in Civilization + Fantastic Worlds + Test of Time
Civilization III + Play the World + Conquests
Civilization IV + Warlords + Beyond the Sword + Colonization (Total conversion)
Civilization V + Gods & Kings + Brave New World
Civilization: Beyond Earth + Rising Tide
Civilization VI

Official related games:
Sid Meier's Colonization
Sid Meier's Alpha Centauri + Alien Crossfire
Civilization Revolution
Civilization Revolution 2
Sid Meier's Starships

Other games:
Civilization: Call to Power
Call to Power II
CivCity: Rome