You could pretty much post the nearly the entire Elder Scrolls sound track so I'll do others.
Mass Effect - Vigil (one of my favorite songs) http://www.youtube.com/watch?v=T7bE3hUwylQ
THIS. THIS. THIS.
My god. When I first got this game and heard this, I just sat at the main menu for like 20 minutes listening to it. Holy crap, if only I could "forget" I ever played this game to experience it again. ><
Edit: For my own personal song outside of the Mass Effect one, I present yet another Final Fantasy XI song like someone posted before.
http://www.youtube.com/watch?v=clld-gFL050 --- Your = belonging to you, you're = you are, their = belonging to them, they're = they are, there = not here.