Free Civ is available online. Up to 126 players. Turns end either when all players have pressed "End turn" or after a fixed intervall (but I did not find out wich values were possible for the interval).
It resembles the single player civ, for example the movement does not stack up multiple turns

Are there any other 4X online games except freeCiv and Empires in Space? There are lots of games which call themselves 4X, but which do not even provide a strategic map to move units on, to explore new regions and meet new players...