FPS
Metro 2033
RPG
the Witcher, a http://www.spiderwebsoftware.com/ game, Kings Bounty, EDIT forgot to recommend you give League of Legends a try it is free to play
RTS
Starcraft II if you are interested in RTS at all it is the game to get
Adventure/Puzzle
Machinarium is just $5 ATM so be quick
@TheVoxelman on twitter