I like cover versions. At least I do when they're doing something interesting with the song. I don't really see the point of recording straight copies of songs - it would be like a tribute band making an album.
A favourite from my old band's set was a disco-funk version of Killing Moon by Echo and the Bunnymen, but I don't have a recording of it.
I've finally got round to making a playlist of my favourite cover versions - in no particular order other than when I thought of them:
Some of them aren't on Spotify, so I've added those ones to a YouTube playlist:
Another list I've got is songs where the original isn't as well known as the cover:
The other list I'd make if I had time is of my favourite sample sources, a best of http://www.whosampled.com/