Consider there are different categories of online games. I can't stand competitive multiplayer, because for some reason it gets me all worked up. I also don't like having people accompany me through the story of a game because I like to have my singleplayer experience uninterrupted by what could potentially completely break immersion.
So far that about covers ever multiplayer game. I must not like them, and I must not play them… but that is where I would be wrong. For one day LittleBigPlanet burst open on me, and kept tempting me to try it's "glorious" multiplayer. It was through this that I found that 99% of the game (and I'm not joking, that is a realistic estimate) is focused on mutiplayer.
It's an incredible offline game. But when you go online you step into a world created by people like you or me. I can see the personality and creativity of hundreds of people at the press of a button, and then meet those people at the press of another button. No killing (most of the time), nothing lost (most of the time), and nothing too time consuming.
Resistance 2 was another awesome online game, that had an extra little game hidden away that was really addicting (although playable in short bursts) and fun. Levelling up, unlocking stuff, and killing the AI creatures was so fun. You just had people around you doing the same thing. No one looses, everyone wins! (Unless you don't utilise your classes special abilities to help your buddies, then everyone dies).
Now I've got a different approach to multiplayer, and am open to almost anything (that works)… weather I will like it or not, depends on the game.