If you're trying to find a game to play on the Web, you can find some pretty good ones with game search engines - search engines specifically focused on finding online games.
If you're looking for Flash-based games, Funlus is a good place to start. You'll also be able to find Jave and Shockwave games here in addition to Flash.
DevMaster is a clearinghouse of sorts for game developers. You can find some great programming resources here for actually writing games - not necessarily finding them. Still, a good resource for anyone interested in games online.
GamePublic scours the Web for anything game-related: news, latest trends, and of course, where to find the best games you can play for free on the Web.
This is a simple search engine for video games put together by MSN Search.
As you can probably guess from the name, FreeOldies is a game search engine that looks for old, outdated games, also known as "abandonware". You can find some pretty interesting games here.