The number of covers I prefer over originals is considerable, so just a few highlights:
Band From TV - Minnie The Moocher (originally Cab Calloway)
Band From TV - You Can't Always Get What You Want (originally Rolling Stones)
Fred Johansson - Music of the Night [http://www.youtube.com/watch?v=X6NYjidHXrk] on Så Ska Det Låta (originally Phantom of the Opera cast)
Elvis - Just about everything, ever
Harry Secombe as Neddie Seagoon - Men of Harlech
Robert Wells & Rhapsody In Rock - Let Me Entertain You
In fact, a whole bunch of covers appearing on Så Ska Det Låta (google it, it's good fun) have been superior - in my view - to the originals. There was a particularly good cover of Mercy, for instance, and Sara Löfgren did a great version of Me And Bobbie McGee.
So yeah. Long list.