Depends on what you mean by 'online game'.. Browser based it has to be this Stock Trading Nation Simulator which is extremely addictive. I even have a diary blog, (or had as I've just been executed for complaining about a RL legal issue). Online Poker is another of my faves, although I tend to play that for a few months then not play for ages. Other than that, I played a little CSS (badly) for a few months and not much else really..
I've started playing Eve Online a few days ago and find it rather interesting. The only problem is the monthly subscription that in my opinion is way expensive. I've heard that you can buy monthly subscription time with in-game money and that players can sell them as well... Can anyone tell me how this works???