Gonzo tagged me with this meme, so I'm going to post videos of a couple of my favorite cover songs. (I don't have a Worst Cover, at least not that I can think of; there's quite a few that I just feel "meh" about, but I don't think I've ever come across a really, truly awful one).
Here's Jimi Hendrix doing Bob Dylan's "All Along the Watchtower":
And here's Save Ferris doing "Come on Eileen" by Dexy's Midnight Runners:
I think both of these pretty much blow the originals out of the water.
(Some runners-up: Evanescence's cover of Nirvana's "Heart-Shaped Box," Fear Factory's version of Gary Numan's "Cars" ... and I had a third runner-up but can't come up with it now. Whatever).
I'm not going to tag anybody; just, as always, whoever feels like doing this, knock yourselves out.