Regular chess servers offer online chess at lightning, blitz, or standard speeds. They are good for playing openings that you need practice with. The Internet Chess Club is without peer, has the most FIDE titled players, the most members, the most events, and is the easiest to play on. But ICC costs a bit. The Free Internet Chess Server with ficsgames is the original chess server. Both chess servers have their share of players who enjoy pretending to play chess, without thought. Their chess is best described as a form of Pachinko. It looks like chess, but is much faster. The other chess game sites are generally buggy, mismanaged, and populated by rude, juvenile computer cheaters posing as chess players.
Databases, chess data
The commercial chess database programs, chessbase and chess assistant are fine, but can be overkill. The free ones, chessdb and scid, are also completely adequate. ChessBase Light is free, but slightly crippled, which may be OK for you. Chessgames.com is a database of historical chess games combined with discussion forums. 365 chess is the biggest chess database online. Chesslive.de is the ChessBase searchable database. (You are storing and reviewing your games in a computer database, right?)
Chess instruction
Learn chess online at IchessU, the #1 place to learn and play chess with chess mentors through a multi-path real-time interactive virtual classroom.