Most people just made something which sounded like the original song.
My favorite one so far is the one by Dr. Kong Balong. It also avoids just sounding like a remix of the original.
The one by Omnitechnomatrix is pretty good too.
Shamefully, the non-Bryan-supplied parts of my song were just stock Soundtrack loops (I wish I could play guitar that well!) and went together in just a few hours.