I love chess. But, having small kids, I do not have enough time to play it on the board. So I play it on the net.
There are plenty of chess sites and I tried quite a lot of them. So ... here are some recommendations.
This article is about places where one plays real-time games, be they blitz, rapid, or slow-time.
Big players
Everybody knows about PlayChess and Internet Chess Club. Both those sites are very good, if I were to pick one, I'd pick Internet Chess Club, I prefer typing 3-letter command to making 30 clicks. PlayChess makes it impossible to view the game history (except saved on the local computer), for me it is noticeable drawback, but those concerned about OTB opponents reviewing their games may like it. Ah, and I hate this room concept which makes it impossible to keep an eye on relayed game while playing my own.
Both those sites are fairly expensive. Both have long history and plenty of users. Finally, both can be used from Linux, but with some difficulty.
From time to time, somebody tries to start new commercial chess site. If such attempt turns somewhat successful, such site usually ends merged with Internet Chess Club, as it recently happened with Chess21, World Chess Network and US Chess Live (WCN and USCL were so far merged into so called World Chess Live, which is just a smaller clone of Internet Chess Club, apart from different admin team and lack of some features there is no difference).
Newer commercial attempts
I know about one new site which have grown enough to require payments: ChessPark. It has one interesting feature - is available directly in the browser (and shows some cute javascript and ajax programming) - but also plenty of bugs (like invalid PGN files with wrong moves wherever promotion or en passant happened). Mostly interesting to those behind firewalls or unable to install client software.
Chess Cube is a very new startup (so far freely available) also aimed at browser-only users. In this case we see fairly interesting Flash application. Just like ChessPark worth looking at, but still rather primitive.
Free (but good) hosts
FICS rocks. This is a place where I play most of my games, this is a site I love, this is a place where I meet people, this is a site for which I wrote some code. And I consider BabasChess to be the best of all chess interfaces I tried (there are a few reasonable Linux interfaces too). Of course, lack of commercial backend means less polish (be it seldom managed website, not-always-friendly admins, lack of GM lessons, or rare updates), but if one wants to play chess and meet people, FICS is an excellent place. And does not cost a single penny (unless one decides to donate something). Finally, apart from chess, one can play chess960, bughouse, crazyhouse, atomic and other variants.
Technically FICS is very similar to Internet Chess Club, the same protocols are behind them, there are very similar concepts and commands, etc. Switching between FICS and ICC is easy.
[ChessPlanet] [chessplanet] has been built by Russian firm Convekta (authors of Chess Assistant), most likely as an attempt to provide alternative to Internet Chess Club. The site is fairly interesting, and reasonably popular in Russia (it is bilingual, Russian and English). Not a place I would pick as my main playing site (especially considering Windows-only client program), but worth playing from time to time.
Recommendations
Never played online, or tried Yahoo! and disliked it? Play on FICS!
Already tried FICS, but you miss very strong opponents, or would like to participate in GM simuls, or need professional support? Try Internet Chess Club.
And don't forget that you are not forced to stick with one site...
Afterward
I wrote more detailed comparison in Polish, if you speak Polish it may be worth a look.