Music / ambient sounds? Very. I find it extremely annoying if a game doesn't get this right, and feel it makes a game far more engrossing if it gets it just right.

If I had to pick a favorite use of music in a game: Blade Runner balcony scene

Music is very important for the atmosphere of the game. I like the music of World of Warcraft for example.

One of my most favorite tracks is https://www.youtube.com/watch?v=FPajwHUx-lw and further tracks from the Curse of Monkey Island OST. Really made the game special for it's time.

One weird thing I've found to be more common than not:

Awful games with rad soundtracks.

Seriously, in what world does Waterworld deserve something this nice?

See Also: Most of the Follin Bros console discography.

Like Cheetahmen? (From Action 52)

Granted, there's only one music track in that game or its sequel, but it's actually a rather nice track, when it works.

(When talking about kusoge, the qualifier "when it works" is often important; in this case, once the music loops, the melody goes missing.)

(Unfortunately, Ultima 5 NES does not have a good soundtrack.)

Very. I'd go as far to say it's what makes half of The Elder Scrolls games (ie, wandering around in silence would get tedious as hell without the amazing Jeremy Soule soundtracks). The Bioshock's would also feel less "late 50's like" without matching soundtracks. I don't replace it. If it's bad I just turn it off. Leliana's Song, Dragon Age Origins.

My favourite is orchestral/symphonic/classical music, as well as acoustic music.

Wargames usually do this especially well; Order of Battle, Gary Grigsby, Panzer Corps 2, Men of War, Hearts of Iron, etc.

Many older RPGs also do this really well, like Morrowind, Nox, Wizardry 8, Planescape: Torment etc.

Music is super-important to me in RPG's & single-player FPS's. It adds so much to the ambience that playing on mute doesn't draw me into the game the same way. Deionarra's Theme - Planescape Torment. It just fit the game so perfectly.

Arena and Daggerfall have great soundtracks, and Jeremy Soule was not involved in either game. (There's a lot of re-used music between them, and unfortunately, dungeons only have ambient sound. Also, Daggerfall does have a bug that can lead to a stuck note.)

Electric guitar gives me headaches.

Also, what do you think of the Crazy Bus theme? (It's a bunch of random (as in, I believe it actually is generated by RNG) notes, and it sounds like garbage.)
https://www.youtube.com/watch?v=sC0cvwnG0Ik


I like orchestral/symphonic music as well, including the soundtracks of such games as Hollow Knight and Fell Seal: Arbiter's Mark.

Wonder Boy: The Dragon's Trap (remake) has a nice soundtrack as well, with an unusual combination of instruments.

As for classical, there's some nice baroque/classical style music in Bloodstained; Holy Wisdom is my favorite track from that game. It has a lot in common with a Bach fugue. (I suspect you were probably thinking romantic-era style music, but it's neat to hear baroque-era or classical-era style music in games, since that's less common.)

Renaissance-era style music can also work well.

I also like music based on folk music, especially klezmer/arabic style music. (Klezmer is rare in video games; I wish there were more of it. Arabic (or what I perceive as Arabic) is more common, particularly in desert levels.) Japanese folk music also works well.

The other type of music I like is chiptune music, particularly when it's trying to imitate those types of music.

Excellent tune, by far my favourite from Planescape. Followed by Annah's Theme and Fall-From-Grace. Mark Morgan's contribution to both Planescape Torment and Fallout was immense, imo. If you listen closely, Annah's Theme has a bit of Many Contrasts (San Francisco, Fallout 2) to it and more of Fallout 2's tribal nature.
Haven't played the game, but I do like There Is No Law Here. Solo Nobre as well.

A couple more.

Really like most of Ari Pulkkinen's music, especially from the Trine games.

Trine 4
Crackling Mire - https://youtu.be/kfo1G8EjqB8?t=3794
Haunted Tombs - https://youtu.be/kfo1G8EjqB8?t=5368

Trine 1
Dragon Graveyard - https://youtu.be/OlPzhQc8e_w?t=808

The King's Bounty series of games also has some great Fantasy music. The tracks were stacking up all the way from Legend to the last Dark Side, so I will be linking to that OST, but know that not all of them are new to that game. Also interesting, the author is using a pseudonym Lind Erebros, while his real name is Mikhail Anatolyevich Kostylev. Many of the tracks only have names in Russian.

King's Bounty - Darkside
A Dark Cave - https://www.youtube.com/watch?v=yrRnaie3mfs
Dreamland - https://www.youtube.com/watch?v=L6Fx5pyGd4g
Dark Campaign - https://www.youtube.com/watch?v=WAF20-e2xt0
Dark Eclipse - https://www.youtube.com/watch?v=YdLVwvdpQFg
Demon Plan - https://www.youtube.com/watch?v=sdohXiY8hZk
Glory Ride - https://www.youtube.com/watch?v=o0QZscAmOcM
Necropolis - https://www.youtube.com/watch?v=wJQA4vooXHw
Valley of a Thousand Rivers - https://www.youtube.com/watch?v=hAVWvygY5qE

But I really got to stop or I would list most of the soundtrack here. It is all some of the best fantasy game music I've heard.

In an instant I was reminded of a Gaelic song, Fear a' Bhàta. Sung by Alison Helzer here.
Marcin Przybyłowicz's The Fields of Ard Skellig takes inspiration from the aforementioned song. The singer, for those interested, is Barbary Grant.
Here is something inspired by Skellige's theme: ''Sea Invocation''. Great voice.

But the point of the thread is sharing. :)

OK, OK... added a few more of the (to me) standout tracks :P

Something similar - Calon Lan (Maid of Sker) fits that haunted hotel theme perfectly.

The music is very important for a game, it set the tone for every moment of the game, and can improves and already great game, we have several examples of this, like Journey with that music that make your skin crawl, of Metal Gear Solid games with that music so iconic that you can separete the game from it's soundtrack, or Silent Hill with their melancholic original score that set the tone perfectly.

Among my favourite soundtrack are:
- Gris.
- Silent Hill (all of them).
- Nier Automata.
- Mass Effect trilogy.
- The Last of Us.
- Journey.
- Doom (1993).
- Bastion.
- Deadly Premonition.