Here's one of the all time great video game songs - the main theme from Chrono Trigger, which in itself is arguably the greatest RPG ever made and is filled with transcending music:
http://www.youtube.com/watch?v=NotILKfI-5o&feature=related
And another great.
http://www.youtube.com/watch?v=WaULITIzS3g&feature=related
Also, another game that has great music, but tends to be pretty underrated is the Half Life 2 games. The music is bleak and cold and fits the opressive theme of the world perfectly and creates a very powerful atmosphere:
Two games beat them all hands down:
CHRONO CROSS and CHRONO TRIGGER.
Chrono Trigger Theme:
http://www.youtube.com/watch?v=8HI5pI0IZgo
Chrono Cross Intro:
http://www.youtube.com/watch?v=GDnPYoGzW78
Chrono Cross - On The Beach of Dreams ~Another World~:
http://www.youtube.com/watch?v=Jn4fzRK8Ze8
Chrono Cross - Radical Dreamers ~Unstolen Jewel~:
http://www.youtube.com/watch?v=7D8Cz9kHYFQ&feature=related
Chrono Cross - Reminiscing ~Unerasable Memory~:
http://www.youtube.com/watch?v=Xu6Avd-pClo&feature=related
this is my favorite song that has ever been in a video game, name what game and you get a gold sticker
i also REALLY like this one
http://www.youtube.com/watch?v=w9YzlEM0PtE
edit earlier post: i just realized that in the page i linked it says what game its from...dangit, so no one gets gold stars for guessing it
Meh. I'm starting to like the tunes from underrated gems such as Fighter's Destiny more-so than most of the overplayed songs I see posted here.
Nostalgia at its best.