Adzeth: I probably played S.T.A.L.K.E.R. wrong, since I didn't get the atmosphere.
AlKim: Worry not, I didn't get it either. There are too many immersion-breakers like enemies that spawn at the same rate you kill them (particularly annoying when they are sitting on a transition point), shitty and repetitive voice acting (the 99 Rads receptionist guy and the scientist bloke spring to mind), the AI, bugs, the faction missions in Clear Sky and
those goddamn loading times. I tried to like Shadows of Chernobyl and failed. I tried to like Clear Sky, but bugs and loading times meant I never got round to finishing it. I doubt I'll give Call of Pripyat a go.
On topic: Planescape: Torment, Baldur's Gate I and II, Mass Effect 1 (not ME2, though), Morrowind, Portal, The Witcher 2, Metroid Prime and pen-and-paper Dungeons & Dragons.
It just depends how oversensitive you are to those sort of things. The game(s) primarily get immersion points from their amazing locales, unique ambience, and overall atmosphere. The glitches and weird voice acting certainly can take you out of the experience.
I don't really understand how you could find Morrowind immersive, but not STALKER, though. It easily has as many immersion-breaking elements, especially in the gameplay (stealth key / book method, anyone?).
OT: The most immersive game I've ever played... hard question. One of the STALKER games would have to go on the list, and probably Amnesia and Penumbra as well. Oh, and we can't forget System Shock 2 and Deus Ex. And back when I first played it, Halflife.
EDIT: Oh my, how could I forget Noctis??