lichess.org

Play chess with a friend, with a random player or with the computer.
It is free. You don't have to register. There are no ads.
Lichess lets you focus on the game by removing all clutter.

Two-player games between humans
Single-player (versus the artificial intelligence, Crafty)
Time controls for chess clocks, including Fischer time settings
User-defined restriction of who can join games, based on player rating
Chess960, also known as Fischer Random, chess variant
Premoves
moretime()
Castling, en passant, and pawn promotion and under-promotion
Detection of check, checkmate, and stalemate
Threefold repetition draw recording (must be claimed by player)
Integrated chat
Visual move validation while choosing destination squares
Game replay and analysis
Spectator mode
Per-game export in portable game notation
Database export of information about all games played by a given person as comma-separated values (CSV)
Translated to fifty languages
Works in any Internet browser (except IE6/IE7), with no Flash and no plugins.