Browse through Steam a bit, build up your wishlist and wait for any of it's sales, mainly summer and winter, same with GOG.
Also, I'd recommend you to keep an eye for the Humble Indie Bundles (not to be confused by the Royale and Gala Indie Bundles, those are crap), lots of neat stuff there.
As for MY personal favorites that I'd recommend you to try, Wolfenstein: Enemy Territory, although a bit old, it's still loads of fun and still has a strong following, it's free and it happens to be the game that introduced me to multiplayer FPS gaming in my PC and one of my favorite games of all time.
Also Team Fortress 2, similar to Enemy Territory, also free and with much better graphics.
League of Legends, free Action-Strategy game with lots of people with anger management issues, but lots of fun nonetheless.
Cave Story, you can download the free version, but I highly recommend you buy the "plus" version from Steam, it improves a lot over the original game and fixes many technical issues the original had.
Dungeons & Dragons Online, great F2P MMO with lots of dungeons and not so many dragons, but quite epic indeed.
Lord of The Rings Online, amazing MMO F2P, from the same studio of DDO and a very different game, but quite amazing too.
Also, there are many free MMOs in Steam, and many of those are great, like Spiral Knights, Star Trek Online, Fallen Earth, Everquest 2, Champions Online, DC Universe Online, Realm of The Mad God and many more. Note that these aren't entirely "free", but they let you play a lot without paying too much or anything at all.