Dodece on 16 October 2007
FPS: Halo 3, Bioshock
TPS: Gears of War
RPG: Oblivion sandbox, KotoR series backwards compatibility linear.
Racing: PGR 4,
Action/adventure: Crackdown
Crackdown basically is a generalist game with elements from many genres. You have platformer, shooter, driver, melee, and RPG elements. There should be something to your liking, and since it is very much a sandbox you can play the game as you like.
Not sure if you have played any of the games in the KotoR series. However they are among the best linear RPGs of all time. You should also be able to find them for a song. So if you haven't gotten to play them yet now would be a good time. Perhaps dated but the story telling, and the character progression give this series so much replay.
