My current favourite site for good online games is http://www.snabbstart.se/onlinespel ... quite a good range of puzzles and strategy games.
If you want something quite special though - and can wait a few weeks - there is a new games site about to be launched. *Special* because it will offer a mix of chat, blogging and games. A games site with IM and MySpace all rolled into one... it promises to be HUGE. More information here: http://www.uvmeplayerslounge.com
One I recently found is www.dungeonrunners.com its kinda like a cheaper looking version of Warcraft, but its also free to play.
An older platform full of free games is http://www.station.sony.com/en/index.vm I reccomend Infantryonline from that one, it you like multi-player scifi shootem ups.
Theres actually tons more around aswell.
try www.bigfishgames.com
www.gamesville.com
www.msngamezone.com
www.gameshouse.com
to name a few
If you put a search in google it will bring up loads more enjoy playing !!