Donkey Kong Country, definitely.
Wipeout XL, though that's not made-for-the-game music.
I'd say X-Wing... but it's hard to say if that really counts. The star wars themes were pretty much ingrained BEFORE I played the game.
Final Fantasy III(6) is good. I never even played the game, and I know half the songs by heart just because I was in the same room where my brother was playing it all the time.
Chrono Trigger had music that really set the mood.
Zelda and Mario both have very memorable themes, but they were such great games music or no, that I think that might just be nostalgia that makes me like the music so much.
And, of course, Tetris... I haven't played tetris since the mid-90s, and I still have days where I wake up with those songs stuck in my head. Dang it, there it is again! :-)