I don't know how they do it, but Civilization games have something... special to them. They're not the most impressive games one way or another, but have you noticed how incredibly hard it is to quit them?
I started with Civ3, loved it and was lucky enough to be in the Conquests beta! What a blast - 4 of the best months of my life (yeah, I know...)
I love getting ahead in tech, and warmongering; hate being the outcast religion: nobody will deal. Actually, dealing with the AIs is not usually fun, unless you have the advantages.
I bought Warlords too, but overpriced. Vassal states a good idea but so nerfed it's more trouble than it's worth.
CivIV is prettier (awesome zoom from space) more depth, good spy system, but I prefer the way Civ3 does some things. Like artillery, and Armies; and the nine Conquests... not to be missed.
Civ3 & 4 and GTA:VC & SA = years of my life.