It's been awhile since I've made a request... I played through part of Donkey Kong Country 2 recently, and I thought that someone could really take Funky Kong's theme from that game and enhance it to sound really cool.
Another game that I think has lots of potential and has yet to ever be covered is King Arthur's World. There are several songs that would reveal themselves to various genre. I think the main track from the "Real World" is called "Forward March" and I like that one. Then there is one that has a funky groove and another one that has a more hip hop type of beat to it. If you haven't heard the music before, you should definitely check it out (the game has its own in game sound test).
To keep the list short, I'll just make it three games. I really like the music in Dr. Mario and I am kind of surprised at how little this game gets covered. I think the more upbeat sounding mixes that I have found sound really nice. So, it would be cool if anyone wanted to cover some more from the two main songs in that game (Fever and Chill).
Okay, just one more: Bubsy! I like the first level music from that game, the music when you get a black shirt is very jazzy, and some of the various other music including the title music. The only mixes I've ever found are based off of a 20 second loop from the game. I might be the only one who likes this music... But if you wanted to find some lesser covered games to try to remix, go for King Arthur's World and Bubsy.