The highest setting I've beat the game on legitimately (space race on, normal settings, standard or larger maps, normal number of rival civs) is Monarch.
I had an Emporer win by domination on a duel sized map, but I don't consider that a legit win; it's too contrived.
I have a few cultural wins on Emporer with space race off, but that deprives the AI of the only way it knows how to win, so I don't count those either.
Now I'm working on how to beat the AI on Emporer setting, large map, standard speed, standard number of Civs, all victory conditions allowed.