I'm only going to talk about original music here.. as fantastic as the OST's for Vice City and Brutal Legend were, I wouldn't classify it as videogame music.
Obviously Nobuo Uematsu has written some incredible stuff. My favourite isn't from a Final Fantasy game but from Lost Odyssey.
http://www.youtube.com/watch?v=qFGrxKDrluI
This song fitted so well with the scene it was in. Best example I can give of music being a large part of a game's feel and memorability.
Also, World of Warcraft. MMO's rarely have great music, and while I've enjoyed Blizzard's previous music, it's never hit me that hard or stuck that firmly in my memory, aside from this track; http://www.youtube.com/watch?v=tqsazZUbt9s
That was the song used in all the trailers, and the log-in screen. Brilliantly written, and totally befitting of the game.
Recently, the theme tune for Cataclysm was released. It's perfect. It's a medley of some of the best-written music in WoW's 6 year history, featuring parts from songs that while you might not have cared that much for them at the time, once you hear their corresponding parts in the medley, you instantly get that flash of memory of where you heard it. The song itself is just grim, as well - brilliant piece of classical music, a lot grittier and more intense than previous Blizzard music; again, perfect for representing the war-torn expansion of Cataclysm.
http://www.youtube.com/watch?v=N-bVd9t2XA0
