This would greatly depend on individual play style. Also keep in mind there are many civs who hardly ever get played, such as Ethiopia & Mali. For me (I mostly play on Epic/Emperor), and the civs I enjoy playing the most (I like tech, trade, wonders, and historical gameplay):
1: Portugal, India
2: England, Netherlands, Russia (3000 BC), Persia, Turkey
3: China (3000 BC), Russia (600 AD), America (good start), Vikings, Greece, Tamils
4: America (bad start), Moors, Arabs, Rome, Japan
5: Prussia, Aztecs
Carthage/Phoenicia is currently being modified so I did not include it (even though it's one of my favorites). But it would be between 1 and 3, I think. Also, I don't really play China on 600 AD, but it is very difficult, probably a 5.