Chrono Trigger - very evocative, mysterious, and oddly haunting - maybe my all-time favourite.
Persona 4 - Perfectly judged, intensely memorable j-pop earwormage.
Fallout 3 - Not so much the songs played on Galaxy News Radio, though they do undoubtedly give the game a unique vibe, but more the ambient soundtrack itself - very atmospheric.
Not coincidentally, these are probably my three favourite games. In terms of use of existing songs, Brutal Legend is worth a mention for its proper old-school heavy metalism - you can't beat haring across the countryside to the strains of 'Kickstart My Heart'. To be honest, the soundtrack was far better than the game. Ocarina of Time definitely deserves an honourable mention for the 'Hyrule Field' tune alone, though I also have a soft spot for the 'Lost Woods' theme.
Edit to add: Can't believe I forgot one of my absolute favourites - the theme tune to 80s arcade machine Rolling Thunder.