Well, I'm very torn. I've played a LOT of fantastic games, mostly from the more recent stable but a few classics as well. (Had an NES and an SNES, but not a lot of games for them and little of note.) I think I'll go with categories.
Best story: Bastion. BAAAAAAAAAAAAAAASTION. PLAY. THIS. GAME.
Best mechanics: Final Fantasy VII. In terms of mechanics, it's the measure by which I grade RPGs. Easy to figure out, simple at its core, difficult but not overly so to master. Why further games DIDN'T use a similar mechanic to Materia (not identical since it's kind of setting-specific, mind you) is beyond me.
Best combined experience: Bioshock. The mechanics are great, the story is great, the game is great. I never had a single moment where I was legitimately dissatisfied.
Also, honorable mention goes to Spec Ops: The Line for totally defying my expectations and actually being fantastic specifically by trying not to be fun. I know that with everyone and their brother saying how great it is and how it really makes you think etc. that it's kind of already cliche, but seriously holy hell that game knocked me off my feet.