The Greeks have pikemen from the go and enhanced scientific research.
Babylon, very strong culture+research combo, no anarchy, plus, the Bowman is quite versatile. Can take out spearmen, archers, chariots, horsemen, etc. etc.
The Maya are very efficient and productive and the enslaved workers are almost as good as normal ones.
Egypt is pretty good too. Chariots are fearsome in the early game.
The Arabs' cavalry is quite scary, and you can just send out a beater or two and hog a lot of early techs, if you add to that the fact that you can change governments very quickly then you can get ahead on the tech race quite fast.