Some of you may know that I occasionally play games on ItsYourTurn.com as "PNE", especially Go-Moku.
A while back, one of my semi-regular opponents said that she was finishing off her current set of games and then leaving the site, but that I could find her at BrainKing.com if I wanted to continue to play her.
I had a look at it and rather like it (I'm "pne" there). They have many of the same games (e.g. chess, checkers, backgammon), though some have different names ("Go-Moku" becomes "Five in Line", for example). Free users have unlimited moves per day, which is nice if you happen to be online at the same time as an opponent and can trade off ten or twenty moves in quick sequence.
One nice feature is the BKR (Brain King Rating, though I always want to read it as Burger King Rating)—a score similar in spirit to the ELO rating used e.g. in chess, which is adjusted according to whether you win or lose a game as well as whether your opponent was stronger than you or not (winning against a weaker player gives you fewer points than winning against a stronger one). I think I like it better then the ladders on IYT, which can be used for a similar thing (people higher up on the ladder tend to be better players).
BrainKing gives you a provision BKR rating for each game but it isn't displayed until you've played several games of a given type (since it would be too unreliable before that) and is only shown in cursive until you've played 25 games of a type. I just got that far recently with Five in Line, where my BKR is now around 1800 (1768 as I write this, though it still goes up and down a little).