Online Training and Playing
ChessMood: A great instructional/training site run by GM Avetik Grigoryan, with content produced by him and other strong GMs. This is currently my main training site.
ChessDojo: Another great training site that I use, run by IM Kostya Kavutskiy, IM David Pruess, and GM Jesse Kraai.
lichess: My go-to site for playing blitz and classical games, but there are also learning and training features, and you can watch streams, play in tournaments, join teams, find a chess coach, etc. Free, and there are no ads or other annoyances.
Chess Tempo: Great for daily tactics training. You can also train endgames, and play games against others, etc. Free, but you can upgrade to unlock more features. An alternative site, which is also free and very good, is chesspuzzle.net.
Chessable: An interesting training site that uses spaced repetition.
There are numerous other sites that are heavily used by many people; I won’t bother listing many others, as there are too many, and I have not used most of them. If you are a beginner, try Chess’n Math, or ChessEdu, or Chess Fox. Other good sites for chess instruction are those of Dan Heisman and GM Alex Colovic, and there are a lot of good book reviews at the site of IM Jeremy Silman. Chess Cafe has an enormous amount of good content.
There are a number of good YouTube sites and blogs/newsletters devoted to chess training and instruction. Some of my favourite ones are produced by GM Noël Studer, ChessMood, IM Junta Ikeda, IM Andras Toth, and FM Nate Solon. If you like podcasts, one of the best for chess is Perpetual Chess, by Ben Johnson. I also enjoy The Chicken Chess Club (GMs Jan Gustafsson, Laurent Fressinet, and Peter Heine Nielsen), and The C-Squared Podcast (GMs Fabiano Caruana and Christian Chirila).
News and Information Sites
The Week in Chess: “Daily Chess News and Games. Weekly digest for download. By Mark Crowther.”
ChessTech: “ChessTech is a free newsletter and website bringing the latest technology news and hands-on knowledge to the international chess community.”
Chess Base: Besides news, this is a full-service web site, with playing area, giant database, lots of instructional material for sale, etc.
A useful database of chess games, both current and historical, can be found at chessgames.com. There is also a daily puzzle, and a database of tournament results.
Good sites for chess history are by Edward Winter and Ken Whyld. Some historical chess ratings can be found here.
For live chess ratings of the top players in the world, see 2700chess.
Tim Krabbe’s Chess Curiosities is quirky, but has a lot of interesting content, including content that will be interesting to devotees of chess problems.
Chess Federations, Clubs, and Tournaments
The International Chess Federation (FIDE) home page is here.
The Chess Federation of Canada (CFC) home page is here.
The US Chess Federation (USCF) home page is here.