I never build Chariots, sure enough.
You should build Horsemen though, not to rush cities but rather for killing units in the field. I often need to kill AI Archers and Horsemen in the open without leaving my attackers exposed, and that's where Horsemen come in.
I also recommend Catapults for the early warfare, especially for weakening AI Spearmen and Swordsmen in the open - if you attack them at full strength even with veteran Swordsmen you will lose a bit too often for it to be economical; you shouldn't be losing your Swordsmen on anything other than mass assaults on cities.