First thing that comes to mind: Anything by Nobu Uematsu (Final Fantasy series). I especially love the music from FF8. Eyes On Me and Waltz to the Moon, particularly.
I also love the old school 8bit sounding music. Super Mario Bros., Legend of Zelda, Street Fighter II.
Other games with sweet tracks are Suikoden Tierkreis, The World Ends With You... Oh lol, the original games for the SNES Super Scope.
Edit:
Oh fuck!!! I just scrolled up. How could I forget Katamari Damacy!? La laaa la la la la la la laaa la la la la la la laaaaaa
Oh and Pilotwings 64, the birdman levels. So mellow and calming. B)