One of my favorite online games is Button Men, a game originally created by the geniuses at Cheapass Games to capitalize on the whole "collectible gaming item" fad of the late 90's. They printed up a bunch of fighters on pin-on buttons, each one holding a collection of dice. You then alternate plays using your dice to capture your opponents dice. Dice have different abilities, some of which make for very interesting game play. There's a semi-complicated scoring system and a lot of strategy, combined with a little luck due to the rolling of the dice. Full rules are at http://www.beatpeopleup.com.
The online game is http://www.buttonmen.com. This is a really sharp version that lets you play with all the buttons, challenging other gamers to one-off games, arena fights, or tournaments. It plays quickly through the web browser, can send you email when games are ready, and can be really challenging.
I'm not an expert player yet; my overall win percentage is around 45%, but oddly for the month of February 2004, I've only won one game, making my monthly ranking pretty pathetic.
If you do check this out, I'm "blicken", and if you challenge me, I'll be glad to explain all the rules.