I have my favorites, and I certainly ignore certain civs out of disinterest historically and gameplay-wise. Generally, I stick to China, Arabia, and the Inca, which suits an empire builder like myself.
Now that BNW has changed certain gameplay features, I expect to play England and France more, and I really appreciate the new play styles of Morocco and the Shoshone.
I would LOVE to play Denmark and Japan more if the developers revamped them into more well-rounded civs. Both are economically strong in reality (without the help of warmongering, I might add), and perhaps a trade route-based UA for both is in order (Denmark made mad money controlling trade access to the Baltic, and Japan is a trade machine). India with a religion buff would be great too.