Well, for real time chess there is:
The Free Internet Chess Server: probably one of the most popular chess servers out there. Just be sure to use the
Babas interface if you join as it is the best one available (also free).
The Internet Chess Club: This one is nearly identical with FICS (it does have a few extras, though) but charges a membership fee. Many grandmasters play here too.
There are some others too, such as Pogo and ChessManiac as well, but the two above are the most popular by far.
For correspondence chess, there are tons. My favorites are:
Chessworld.net: Probably the most active cc chess site on the net, partly because it is loaded with some nice features. While you can play for free, a membership is required to enjoy all its features.
Red Hot Pawn: Also a very nice and active chess site. Like Chessworld, a membership is required to get all the features but the free account is rather nice.
It's Your Turn: A nice, free site with all sorts of games. It has a basic chess section with some variants (we used it here to run our chess tourney). Games aren't rated, though.
Chess.com: This is a new site that has been making a name for itself. Besides having a free and nicely functional cc chess system, it is also a site loaded with news, blogs, chess articles and active forums and even its own email system. I recently joined and really like what I have seen so far (albeit, the notification system to alert you when it is your turn seems to be on the blink). I think as they squash all the bugs, this place could be formidable. Also, live chess is coming soon as well!
Hope these help.