Yucata is a good one. It's designed for turn based games rather than live games and ones where everyone takes their turn simultaneously. It's almost exclusively card games.
You can play multiple games at once; if you're on turn in a number of different games, you can easily click through each of them and make your turns.
Games can take a number of days to finish. I tend to log on every few hours and make all my turns; if my opponent is also logged on we might get a few turns in each, otherwise just the one until a few hours later. Providing you're ok with playing like that, it works great (e.g. as a distraction from work...)
It is possible to play live games (either with friends, or with strangers by requesting a live opponent), but there is no way to ensure your opponent plays live i.e. there are no time limits for turns.
I didn't know most of the games on there, but it's been nice to learn some new ones.
Finally, there's a cool level/points based system; if you're the kind of person who likes getting Stack Exchange badges, you'll enjoy this feature.
I also back BGA too, as the other comment recommends.