The first Driver game. The song that played during the driving test, and a few other times throughout the game. I've looked for somewhere to download it but without any luck.

Halo 2 theme song- Blow Me Away by Breaking Benjamins

Castlevania 3 on the NES
Chrono Trigger
Demon's Crest on SNES
Tomb Raider 1(I hate the game and love the music)
Donkey Kong Country 1
Final Fantasy VIII was really well done.
Soul Blade on PS1
(I'm getting nostalgic so I'll stop now....good times, man...good times.)

Any of the Silent Hill soundtracks would be my choice. I can't really name a single song on any of them that jumps out at me, but Yamaoka's trip-hop/ambient/experimental work is amazing, and stands above most other video game music as actually listenable on its own.

In fact, that's one of the two ways I judge good video game music: whether or not you want to listen to it out of the context of whatever game it was in. A few other games jump out at me in that respect: Beyond Good & Evil, the Digital Devil Saga games, and Rez. The other way is whether the music adds to the overall atmosphere of the game, the honor of which would probably go to Super Mario 64, Donkey Kong Country, Eternal Darkness, and a few others I can't think of at the moment.

For me, the all-time favorites are Final Fantasy VI (other final Fantasy were pretty good too, Nobuo Uematsu is a genius), especially Terra´s Theme (I think that´s the name) and the theme song for Suikoden II (Playstation). Metal Gear Solid is good too.