If we're just talking games with good atmosphere/immersion:
Penumbra
Alone in the Dark
Planescape
Bioshock
Half Life
Aliens vs Predator (the newest one)
Minecraft, when you're deep in a mining tunnel and you can hear a zombie nearby and you're walking catiously and HOLY FUCK A TINY SPIDER IS EATING MY LIVER OH GOD ITS-creepersplosion- *you have died*
Heh, yeah, I wish I liked horror games, alot of them have great atmospheres. Might look into AvP, doubt I'll ever play Planescape, I've recently been trying to play Bauldur's Gate 2 and I just can't get into it.
let me be the odd duck and recommend Arma 2. It's first person and immersive. Lots of things going about their own agenda. All of this is moot if you can't auto-correct the awful(read AWFUL) voice/dialogue. It's an immersive sim.
I LOVE Arma 2, my old computer could never run it well and I completely forgot about the game after I upgraded, thanks for reminding me.
Mafia 2 had a great feeling of the world about it, especially watching the seasons changing to winter and the whole world adjusting to the weather. Just being in the world was more fun than playing the game.
Weather is one of my favourite things in games and I always feel its never used as much as it should be. Will definitely look into this, another game I forgot about after I upgraded.
Fpp with good immersion you say ?
Deus Ex - First one would be the best choice
Dark Messiah of Might and Magic - I don't know why this game got nearly no attention, it's just great.
Loved both, I have DM of MnM siting on my desk right now, actually.
I will add Metro 2033
EDIT: I want to second Mafia 2, WAAAAY too short and totally linear but what was there was very cool feeling. They could have done so much more with this by making the world live and breathe, but still totally atmospheric. When it changed to winter in the 40's i got all Christmasy feeling, pretty cool.
In the process of playing Metro actually, I got it a few weeks ago when it went on sale, I love it.