Sadly I have a very...
VERY limited perspective as the only one I've played is Civ. Rev.
That said I wanted to stop by just to express that I really, really enjoy the game and wish I had a better PC so I could play some of the other Civ games.
As for my favorite civilization in the game, it's hard to say...they all have pretty good bonuses. As such I tend to play as Random. That said, if I HAD to pick one over the rest, I'd have to go with the Aztecs. Their ability to fully heal armies after every victory is
obscenely good. It makes it so that if someone's trying to take a city, they have to take out your defenders with a single attack, or the next group of attackers will be fighting the full force of those same defenders. And since (generally speaking) defensive units have a very strong advantage when defending a city, you can just stick maybe 2 armies of them for defense rather than having to put in 4 or 5.
The Indians are a lot of fun too, though. The fact that they start the game able to use all special resources is very useful, especially if you're lucky enough to start with some Dye or Gems or Gold or something near your capital city. Dye in particular since it can give you a very good head-start on early-game research.
Then again, the Japanese are really nice too. Their cities come with built-in harbors, making for fast population growth. And who doesn't like having some Samurai Knights, right?
Then there's the Greeks with their half-price Famous People, starting the game with a Courthouse and Democracy as their base-government.
The Mongols kick ass for rushing, but it's easy to over extend yourself if you convert too many barbarian villages and have no units to defend yourself with.
See what I mean? It's hard to pick just one when they all have such great stuff going for them. But yeah, in the end I've gotta go with the Aztecs.