I suppose for me it's RPGs and Story led games, so anything with a good story and decent game mechanics no matter the genre. I especially like WRPGs where you have an influence on events, or at least the illusion of influence.
RPG: All things Bioware, Bethesda and Obsidian (Dragon Age, KoToR, Neverwinter Nights, Mass Effect and a lot of older RPGs... and CDProjeckt may make the list soon)... and Deus Ex.
FPS: Deus Ex, Half-Life series
Adventure: Prince of Persia, Tomb Raider, Uncharted, Zelda
I play all types of games but these are the sort of games that impress me the most.