Playing board games and card games online can be a lot of fun, no matter what style of games you like best. These are the best places I've found to play board games and card games online.
Games.com is the official place to play many Milton Bradley, Parker Brothers and Hasbro games online. Their lineup includes Boggle, Clue, Monopoly, Scrabble and Yahtzee. They also offer traditional board games (Chess, Checkers), card games (Hearts, Rook), and arcade games (Asteroids, Missile Command).
BSW is a site that offers the ability to play designer (aka German) games online. Games available include Settlers of Catan, Carcassonne, Can't Stop, Liar's Dice (Bluff), Ra, Web of Power and many more. This link takes you directly to BSW, but many first-time players will want to read one or all of the assistance guides available in "Related Resources" below, since the site is mostly in German. (There are plenty of English-speaking players to be found, however.)
The thing that makes ItsYourTurn.com unique is that you only take one turn at a time -- so you and your opponents don't have to be online at the same time. Backgammon, Battleboats, Chess, Checkers, Go, Reversi and Sabotage (a Stratego-like game with some nice twists) are among the games available.