The main theme music from Rad Racer (NES, 1987) is really under-appreciated, I think. Although that may be because it was one of my favorite games as a kid. I'm pretty sure the composer was Nobuo Uematsu. I think a rock or metal remix would be awesome, maybe with some electronic or techno elements.
http://www.vgmusic.com/music/console/nintendo/nes/RR_Music1.mid
The other themes aren't bad either, though they aren't really that interesting on their own. Maybe parts of them could be combined with the previous theme.
http://www.vgmusic.com/music/console/nintendo/nes/RR_Music2.mid
http://www.vgmusic.com/music/console/nintendo/nes/RR_Music3.mid
And here's a video of some of the gameplay. (this game was devilishly hard, I rarely made it past the third course, since running into anything more than once was like game over)
http://www.youtube.com/watch?v=DlsVgwjFoeQ
(by the way, this was the music on the Strong Bad episode where he becomes an anime character, if any of you have seen it).