Aaaah, I love game music. /supernerd
Some favourites of mine are already mentioned, Diablo 1's Tristram, Unreal (
Night Vision is such a rush!) and the Fallout games.
I have a fair mp3 collection of game music and still play them often.

Here are some others that I worship:
Dungeon Keeper. A wonderful intro, soothingly sweet cynical map screen and awesome in-game ambience.
Crusader: No Remorse, with the track starting at 29:49 being my favourite.
It makes you forget that the game is made on a tweaked world-of-suck Ultima 8 engine and forgive its poor response in controls.
Command and conquer; although all C&C games have great music (well, the ones made by Westwood, with Frank Klepacki as the music artist), my favourite is the first game, with the track at 6:00. Daka daka. Dak dak dak dak. Daka daka.
The Eye of the Beholder 2 intro. Probably the only midi in the world that shivers my spine. Epic finale. (Except not in that video, since that heathen cut the last 5 seconds off.)
Dune. Several things can be said about the game. I think it was a nice game, even though it had nothing to do with the book. But the music is simply awesome, it has to be agreed upon that.
My favourite is 'Too', played when you take off in an ornithopter. (15:26)
Dune II. Frank Klepacki. I'll build him a statue someday. Also,
one of the most epic game intros ever made.
Homeworld. Starting from the menu and wonderful first mission music all the way to the dramatic ending symphony Adagio for Strings and the band Yes doing an epic song for the credits. It's a musical masterpiece of suspense. Not all tracks are present in that youtube list unfortunately.
Lands of Lore 2. My favourite is the one in the link, Claw Mountains, although it's quite depressing. Unfortunately not all tracks are listed there. Weird game. Perhaps not even a very good game, but Frank Klepacki (there's that name again) made an epic soundtrack for it. A pity the Dark Halls are not in that list, although one has to play the game to fully understand how bloody scary it is.
Luther... we're coming for you...Fallout 2. I had to list one of my favourite tracks, Dream Town. So much death and destruction in that game. But here is this little quiet town, where time has stood still, everyone's leading simple lives and life is good... or is it?
Quake's intro, <3 NIN.
Doom. The idea was to have music and ambience a la Quake in Doom, but for a reason I forgot they went with normal music instead, performed by Bobby Prince. I am glad they made that decision.
The one in the link is not my favourite tune, but E2M2 is by far my favourite level.
Goblins 3, I think I am going to label this track as cute.
Alone in the Dark. Imagine playing that game while being a little kid. No wonder I'm not completely right in the head.
Mr. Do's Castle. We had a Commodore 64 when I was little. Crashing large bricks on top of big googley-eyed monsters never got old. And neither did that track.
Enigma Force. Speaking of Commodore 64 games, here's another favourite. Unfortunately I never played through that game because it was too complicated for little kids.
I can post so many more, but I don't want to have this forum run out of server disk space. So many good old games with good old game music.
I'm glad I am an old guy, having witnessed the golden age of gaming, when large corporations like Activision and EA were still small and not satanically evil.
Thanks for starting this thread so I could take a trip through time.

(
The Last Ninja! Awesome!)