One of the first games that regularly pops into my mind when talking about sound is Quake. I've always found its sound effects outstanding: from the weapons, to the monsters, to the ambient (the portals), they're gritty, powerful, extremely effective and memorable.
Another game series that attains top score in my book in terms of sound is Thief, especially the first two instalments. Both eerie and realistic, not only the effects are crucial in setting the atmosphere, they also play a very important role in gameplay.
Doom, of course, sports some wonderful effects that have made history (doors, lifts, monsters... I especially dig the Cacodemon's gurgling death sound :) )
I have to mention Valve games as well: both the Half-Life and Portal series feature original and iconic sound fx, that have achieved meme status.
Why not talk about older computers... on the Amiga, I've always stood in admiration of the effects in a couple of Bitmap Brothers games: Gods and Speedball 2 ("ice cream..."). And on the C64, I'd like to mention Strangeloop, Paradroid, Nebulus (aka Tower Toppler), the classic takeoff sequence from Raid Over Moscow... and the famous scream from Impossible Mission, of course!

I'm playing Extraction Point right now... it's hard not to agree.

I wonder if there are also completely silent games for deaf people? Of course you can always just turn the volume to zero, but that is basically CHEATING!

Music: Ultima 7 and the fan remake Ultima 5: Lazarus
Followed by the first Monkey Island

Ambient sound: I agree with the choice of F.E.A.R. and I would add Amnesia The Dark Descent, which often works more via hearing than via seeing because you are so busy hiding.

That's good to hear. I haven't gotten around to playing thru it yet.

I think I might actually prefer the original Ultima 5 soundtrack, provided you find a version where it's fully intact. (The DOS version lacks sound, as does the Commodore 64 version (though there's music if you play it on a Commodore 128). The Amiga has only a single song that plays through the entire song (and isn't part of the soundtrack of other versions), as does the NES version (except for the title screen, intro, and ending), with the NES version being legendarily awful.)
Making a video game deaf accessible is relatively easy. All you need to do is make sure that there aren't any important audio cues that aren't also displayed visibly. Also, if there's spoken dialog, the game needs good subtitles, and the subtitles really should be enabled by default (something like 96% of players will leave subtitles enabled if they're enabled by default, and something like 60% of players enable them if they're not enabled by default).

Of course, there's still games that aren't deaf accessible, or that are only partially deaf accessible. One example I've recently seen in a speedrun comes up in Kirby's Dream Land 3; to get the true ending, among other things, you need to complete some minigames. Unfortunately, one of those minigames relies solely on audio, making it essentially impossible for a deaf version to complete, as you have to make 3 correct choices in a row, and with 5 options each time, your chance of getting them all if you're deaf (or playing without sound) is only 1/125.

Deaf people don't really need absolutely silent games, just more well done subtitles + audio cues. Eg, in Dishonored the 1-2-3 lightning bolts above enemies heads showing level of alertness goes a long way in making even action / stealth games playable. What are mostly unplayable for deaf people are games with no subtitles (though can sometimes be awkwardly worked around to an extent by ALT-TABBing out to a walkthrough that contains a transcript) and particularly audio based puzzles (eg, in Myst or the 'Jungle' section of The Witness).

Definitely have to agree that FEAR has excellent immersive sound design.

I love fighting the mancubus in Doom 2, specifically for the sound it makes. Hearing the arch-vile also makes me a little nervous.

I saw a game over montage for the Amiga version of Mistress of the Dark. I was impressed at how good the music was, considering it was a computer from the 80's.

The Thief games come to mind.

I played the series two years ago and I still remember the sound effects. It's that good.

The iMUSE system in TIE Fighter was pretty great at making the music fit the action on screen.

Silent Hill, especially the first two games, unique and now iconic sound design

Believe it or not, I've still got to play Doom 2 - actually I've only recently finished the first one! I'm looking forward to it.
(the sound of the Big Sisters in Bioshock 2 is enough to make one nervous, too, I think)

The weapons, explosions, shattering glass... they're especially crisp, full-bodied, impactful - I like them!

I played Forgive me Father recently and the shotgun was one of the best BOOMS I've heard in a while.