There are a lot of places to play chess online, but for me, there are two that I like the best. Both of these sites are very close in a lot of ways, but there are also some differences.
Personally, I don’t like playing on sites where the board or pieces are small or hard to interpret and both of these sites have great graphic interfaces to play on. You can choose from a number of board and piece combinations, size the board from small to large, and play in 2-D or 3-D format.
Both sites also have the option for you to receive an email of any of the games you played so you can analyze them and find your mistakes. This, along with the option of observing the play of highly-rated players, are two of the best ways I know of to improve your game.
The ICC is a busier site, many times with as many as 3,000 players and 100,000 games played per day. It does cost $59.95 per year, which is a pretty good deal considering all that you get.
You can sign up for a free 7-day trial to see if you like it before you pay. They have a huge variety of live online events for members, including lectures, chess lessons, simultaneous exhibitions, tournaments and much more.
FICS has over 300,000 registered users and offers many of the same benefits of the ICC. They also have many fine interfaces that may be downloaded, or you can use the Jinapplet if you do not wish to download a graphical interface. The biggest difference is the FICS site is totally and completely free for all players.
Both sites offer the relayed games of any major chess tournament, unlimited play and great support staffs.
You’ll have no problem finding a game as well as strong competition on either site, so you can be playing and and improving your chess immediately.