Well I think mine could be Travian but maybe Army Commander. If you had asked me that 3 years ago I would have said club penguin. I also like the Percy Jackson online game though it always freezes. So I'm not sure.
I think I may not understand the limitations of the question. Are we talking about games that only exist online--like flash, free-content and MMORPGS? Or are we also including games that can do either--like Wolfenstein and Assassin's Creed? If it's the former, I would say NFS world is probably my favorite at the moment.