Yahoo! has games you can play online at
http://games.yahoo.com/ such as Backgammon, Chess, Checkers, Poker, Blackjack, Bridge, etc.
A good directory of games can be found at
http://dmoz.org/Games/ & web enabled games at
http://dmoz.org/Games/Webgames/
I personally like strategy war games that can be played online. They can be quite time consuming though, so I don't play very often. These are the ones I've played:
Command & Conquer
Total Annihilation
StarCraft
If you're into role playing games,
Ultima Online looks pretty cool. I've never played it, but read about it. This one IS a virtual online world. Thousands of people are connected to the same game simultaneously, with their actions having lasting effects within this game world. Some people go on adventures with groups of players in the game (into the dungeons!), others build & maintain stores in this online world.
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John Hammell
Network Administrator, GreekChat.com