What are some of the best sites for online chess?
Free sites with friendly communities are better.
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Chess.com has become a hot spot, with live and correspondence chess, along with tactical problems, articles, etc. The live chess is OK, but not the best.
ICC or playchess are the best for live chess, FICS if you want free, but it doesn't have as many titled players or features. Those sites will also have video's, live commentary of top level tournaments, and much more.
If you would like to play a lot of quick games, I would recommend FICS, or the Free Internet Chess Server. Using a good interface like BabasChess or Winboard, it's response time is a lot crisper. It has a long history with a lot of "culture", off-topic chat channels, 'bots', and a lot more master level players that some of the other sites.
Chess.com is also a good option.
ChessCube has one of the nicest user interfaces, although it cannot be used with iPhone or iPads since it uses flash.
Chess.com is very popular and free. It also has a Facebook app that you can use to play. You can also play with a time limit of days/weeks and this is very useful if you rarely can find the time to sit down and have a serious game straight.
Red Hot Pawn has a great chess community and is available for free, or with a paid subscription.