Favorite, or more often?
It's a tough question though, there's many (well, many I played often for a time). I played Mass Effect 3's multi-player for 1,100+ hours at this point. I also played Diablo 2 for about seven years of my life (approximately four of those online), so I suppose that ultimately Diablo 2 has been my absolute favorite online game of all time (if I just go by amount of time dedicated to it, and also by fun). Although, of course, Diablo 2 cannot be considering 'strictly' an online game, it's primarily offline (in my book anyway) but it had a good online mode and was well supported by the devs. I also played the first Natural Selection (Half-Life modification) back when it was relatively new, for a period of about one year and a half or so. I played the first Left 4 Dead from release to the month they released the sequel (so about a year or so). I also played TF2 for a good two years (one of which almost constantly, at least one session of 1 or 2 hours per day, every single day for months without exception; that was back when it was released as part of the Orange Box, prior to when they started to add new weapons and major updates).
Lately, the online game I'm playing the most often is The Old Republic, simply because I'm entirely new to the game (thanks to the latest update). I like it, it plays very well as a single-player game (I.E. it's online, it's an MMORPG, but you can literally play it as you would a single-player, ignoring side quests, only doing Planet and Class quests to follow the story line like you would in a game like Mass Effect or Dragon Age). I'm planning to finish all eight Classes' respective story lines, then I'll stop for a couple of months until they've completed enough "Episodes" of their new story line that's supposed to be worked on for another year (and they'll release new episodes every 1 or 2 months I've heard). I'll probably also start playing Diablo 3 often enough once their next update goes live (it'll last maybe one month total then I'll move on to something else, since Diablo 3 has never been able to keep me interesting for more than about a month at a time, but it's ok I'm enjoying it in small bursts). So, yeah, right now The Old Republic is really fun (I don't play it every single day, but lately it's the one online game I play the most anyway).