Link's Awakening
Gabriel Knight (all)
Metroid Prime
Mario Sunshine
Wind Waker
Resident Evil 4

Silent Hill
Bioshock
F.E.A.R
S.T.A.L.K.E.R
Dead Space
Alan Wake
Demon's Souls
Ico
Shadows of the Colossus
Journey
Red Dead Redemption
The Elder Scrolls V: Skyrim

'X-Com UFO Enemy Unknown'. The original 1994 Mythos Games version. Intense gameplay and absolutely incredible music/audio.

'Oddworld: Abe's Oddysee'. Again, intense gameplay and with a character you cared about. Excellent audio/sound, and overly aggressive enemies. A beautiful game.

I don't know if I have played any atmospheric games to be honest or games that have felt very atmospheric.

Another World.

The game teleports you really into another world.One of the first using polygons.
A really interessting new world and great story.A very special gameplay(one shot=you're dead)
A great ending.(a great intro)

Omicron

A similar plot like another world/great atmosphere

Sotc
You ride on the horse for half an hour or more without trying to do something and you won't get bored,because the atmosphere is amazing

Little big adventure
The game looks like a nintendo game,but it turns into a great story about dictatorship and friendship.

Heavy Rain

Not a masterpiece in design,but the atmosphere will get you for sure(as long as you don't start playing the game just with the purpose to criticize the unusual controls)

Legacy of Kain
amazing how atmospheric a 2d game can be(same with SOTN)

Metroid Prime because you are totaly alone in this alien hostile world, wandering in silence.

Honorable mention to the first Bioshock for similar reasons.

Stalker series on PC and by a wide margin. Most underrated games ever. It's too bad so many console gamers never got to see how great this series really was.

ZombiU

DooM 64

Metroid Prime 2 Echoes

I really have a thing for that atmosphere of desolation and loneliness found in the Metroid Prime games and Shadow of the Colossus. Being alone in a strange world, often surrounded by the remains of dead civilizations, it's just so beautiful in a sad and haunting way.

Resident Evil 4 and Bioshock also get a mention for mixing the aforementioned feeling with horror elements to great effect, as does Dead Space for its emulation of classic late 70s/early 80s sci-fi horror, and Xenoblade for creating such a great sense of wonder and adventure. (Xenoblade spoilers: The space segment at the end of the game, before the final boss, made my jaw fall THROUGH the floor)

Metroid Prime, Metro, Max Payne