Well I narrowed it down to a lot of thought, and I finally picked Rome.
Rome because of their very good UU's, and an effective UA. Their classical era power is immense, and they get an enormous early game boost from producing buildings 25% faster.
A close second is the very popular hit, Persia. These two I narrowed it down to for my final picks. But I chose Rome, because when you look at it, what's better: A common 20% production boost, or an everlasting 25% production boost. I wouldn't get into a big stance on Rome being always better, both civs are both extremely good in most situations.
My most notable honorable mention, India. In Civ4 India was my favorite civ. For about a whole year on Civ4 all I played as was as Asoka. And I loved it. I still love India on this game, despite their useless UU and a rather weak UB. Their UA makes up for that though, which is probably my favorite UA in the game. All that's required is Forbidden Palace, and later on, and Order policy, and you've got probably the most effective ICS in the game on your hands. Late game explosion, that is India.
Other honorable mentions for me include the lord of wealth, Askia of Songhai.
The perfect balance, China.
And the guaranteed cultural win, France.