They were very quickly conquered by Spain, which is their biggest effect on history - Spanish dominance in America. In the game it almost never happens, so their situation is a bit weird, remaining as a backwards nation till the end of the game.
I like how they're handled in Europa Universalis 2, my favourite global strategy game - when Spain conquers Cuzco or Tenochtithlan they annex the entire country. This is of course very restrictive to other colonial nations, but it is a historically deterministic game to some extend. In Civ I'd prefer them as strong barbarians.