The Settlers Of Catan

Another board game made into online game, and this one's great. It's a bit complicated if you haven't played before, and the computer players are sometimes a bit annoying and gang up on you, but on the whole this game is really well made. You can play a game of Settlers that would normally take over an hour with human opponents in ten minutes!
You can also play against other people, but it helps to play with people you know won't take ages over their go. I don't think you can get the rules from Wikipedia (probably due to copyright), so you'll have to pick it up by playing.