Well I've always been a *huge* fan of Oceania, and as such, I'd love to see the Hawaiians in the game. Or at least the Polynesians in general. They were incredible seafaring folk, and the Hawaiian Monarchy was a recognized independent power for a time, before the U.S. 'culturally absorbed' it.
Other than that, I believe the civilization of Mali was quite astonishing for its time. Europeans were astounded by the empire, it's vast riches, and incredible commercial trade. Not much for science or military, but they could scam the fillings out of your teeth. It was also quite large.
The Anasazi may be a good choice, but I think Native America is more than represented by now...
Catholics could be interesting. Not an empire in the technical sense, but arguably, it has held more power than any other civilizations in the game. They built wonders, held cities, had leaders and such, so you could count them... I s'pose. It'd be a stretch.
Portugese is a likely choice, but they're boring. Same with Italy, no offense intended. Too many European civs already.
And I suppose that's all I have to say. I'll shut my trap now ^_^