Found this the other day, Deanej has finished (well at least to the point at which he is comfortable to release it as a finished project) a Star Trek Mod for Civilization IV: Beyond the Sword. The game comes with a standard, multi-era game, stretching from ENT (briefly) to VOY. Along with several additional mods focusing on other aspects, Enterprise in general, the Xindi Attack in specific. TOS in general, TNG in General, Deep Space Nine in General. There's also one titled Klingon. ATM I have only played the standard multi era game, and have not finished anything.
14 races: 19 leaders
United Federation of Planets: Jonathan Archer (Phi/Org), Admiral Leyton (Org/Pro)
The Klingon Empire: Gowron (Ind/Pro), Martok (Agg/Chm)
The Romulan Star Empire: Neral (Agg/Org), Shinzon (Agg/Ind)
The Borg Collective: Borg Queen (Exp/Ind), Locutus (Exp/Org)
The Ferengi Alliance: Rom (Phi/Spi), Zek (Fin/Chm)
Breen Confederacy: Thor Gor (Agg/Pro)
Cardassian Union: Gul Dukat (Agg/Imp)
Third Republic of Bajor: Shakaar (Spi/Org)
The Dominion: Female Changeling (Org/Imp)
Devore Imperium: Kashyk (Fin/Pro)
Kazon Collective: Maje Culle (Agg/Exp)
Krenim Imperium: Annorax (Phi/Agg)
Nineteen Tribes of Hirogrn: Decaran (Agg/Spi)
Vidiian Solidarity: Denara Pel (Phi/Cre)
All of the ships are race specific although they'll say Light I, Light II etc... They are just dressed up like Federation, Klingon, Romulan. Obviously the Federation, klingons, romulans and Cardassians have the most differences, but you wont find a federation ship in the Kazon fleet (unless you capture a federation planet and build the unique federation unit, the constitution.)
Edit: might help if I have the link...
http://forums.civfanatics.com/showthread.php?t=233074