It's so hard to pick, honestly. Music is so amazing and I'm endlessly overjoyed that (some) game companies haven't forgotten how integral music should be to an overall gaming experience.
Back when I was a kid, even with its (let's face it) really poor sound processor, the Genesis (Megadrive for people in the UK? Is that right? Sega's system, anyway) was home to the Sonic games, which had some of the most awesome videogame music ever.
This is my favorite (Sorry I don't know how to embed videos hurr):
Flying Battery! [http://www.youtube.com/watch?v=_T7hdIh-gtw]
Oh man... when the melody kicks in at about 28 seconds? Makes my head tingle every time.
In moderns games, though, I am often surprised and delighted when music elevates an otherwise enjoyable experience to something really immersive. Nier was like that for me (I enjoyed the hell out of that game, even if no one else did).
I know it's really cliche, but Akira Yamaoka is probably my favorite musician for games, even though I am actually not a big Silent Hill fan. He just does such a great job and has a very unique sound that suits his subject matter perfectly.