Backgammon
Backgammon is one of the oldest games in the world, and it's going strong on online sites. Sites like Itsyourturn.com offer backgammon as one of many turn-based board games that you can play for free. Players can either play games in real time or take turns at long-term games with one move per day.
Scrabble
There are many Scrabble-line games on the internet for word game fans. Braingamez.com has an excellent interface where you play with another player live, taking turns placing letters and making words.The scoring is the same as the board game, and the game runs very smoothly.
Bingo
There are dozens of sites online on which to play Bingo, but a lot of them are turning into pay sites, similar to the gambling Poker game sites. For a totally free Bingo game with conversations, try Pogo.com. You will need to sign up with a username and password, but you can play on the free level.
MMORPGs
Massive Multiplayer Online Role Playing Games, or MMORPGs, are among the most popular games to play online with others. You join a game and create a character. You then exist in the world of the game as your character, having adventures, interacting with other characters and earning riches and rewards. These games can be set in any environment, from Star Trek and Star Wars to medieval times and war time.