Text Based Games
These might not be too popular, but some people are crazy for these games. I used to be one of them. Got really addicted to this one online text based game, called dominion.
It requires you to be online now and then, every 12 hours or so, so you can construct your buildings, and train your army. It's a pretty competitve game, and you're competing against 7000 players. Whosever dominion prevails, is on top, wins.
Got any others?