Well, you'll probably want to try League of Legends, one of the bigger games out there and a kind of genre that's foreign to console.
Battle for Wesnoth is a fun turn based game with RPG Elements.
http://wesnoth.org/
Team Fortress 2 is my favorite multiplayer shooter by far.
DC Universe Online is pretty fun as far as an MMORPG Beat em up goes... you can always buy more stuff but it's fine at base level really.
Global Agenda is also like that, but more shooty. Those three i'd suggest getting through Steam who will have a lot of free to play games and some great sales when you decide to drop some money.
http://store.steampowered.com/
Though a flash game Super Mario crossover is a lot more fun then you'd expect.
http://www.explodingrabbit.com/games/super-mario-bros-crossover
Hm that's all i got for right now.
