The Best Games

 With over 100 million members, chess.com is the internet's biggest online chess community. You can play both live chess at various time controls, or correspondence-style games with days per move. Basic membership is free, but premium users gain access to extra training features, videos, and statistics. 

 Lichess is notable for being a free and open source online chess server. You can even embed it in your own website. It provides a variety of online play modes, as well as training features, and the competition is decent. Although it lacks the training content of chess24 and chess.com, Lichess has a slick and fast interface and round the clock tournaments.