Galactic Civilizations, as the name suggests, is similar to Civ., but has you building a futuristic space empire, as does Master of Orion, although the latter is a little old now and the most recent version MOO 3 was not very highly regarded.
Spartan is an empire building game set in ancient Greece.
If your tastes extend to fantasy the venerable Masters of Magic is very good and shares quite a few ideas with Civ, such as building settlers to found new towns, researching magic, instead of technology etc. and runs fine in DOSbox. Dominions 2 is also a good fantasy empire builder (the graphics are pretty dated though), but has no diplomacy in single player, so you'll have to go multiplayer, if this is important to you.
Others have mentioned EU and EU2, which are real time rather turn based, but aren't the typical RTS clickfest.
Edit to fix typos and add: Paradox have also recently released Crusader Kings, which appears to be EU for Medieval Europe and looks like it might be interesting.