In reply to gd303uk:
Jennifer Warnes' "Famous Blue Raincoat" album is a collection of Leonard Cohen covers, and almost all of her versions and arrangements are superior to Laughing Len's originals. Nirvana's unplugged session also included a sublime version of "Man who sold the world" and, of course, a totally arresting and head-turning cover of "Where did you sleep last night?".
One for the wilfully obtuse or perverse, but Duran Duran's cover of "Perfect Day" by Lou Reed is, again, superior to the original. Even Reed himself has acknowledged this, and the rather woozy version that Simon and the boys recorded show that they understood what they were doing and the type of song "Perfect Day" really is.
Though it has to be said that their version of Public Enemy's "911 is a joke" really really DOES have to be heard to be believed. Jaw-droppingly awful and almost bizarre in its misguidedness. Rich and fat Simon half-rapping and singing about the police not answering his emergency call and getting to his gated mansion house quickly enough.