I don't know if it counts as it is his own song, but Eric Clapton doing 'Layla' as a sleazy blues number on the 'Unplugged' album.... not a guitar riff to be recognised, no electric instruments, just him, an accoustic and some gentle backing..... and a whole lot sexier song as a result......

On the reverse, I think the Animals version of 'House of the Rising Sun' is a lot better than the original (can't remember if it's Woody Guthrie or one other of that era that I've got a recording of), but somehow, it isn't actually much faster, just more energetic.

LTS