I saw this link on Digg that said "Neil Young sings 'Fresh Prince'" (or something similar) and was instantly hooked. I love covers, especially when someone completely outside the genre of the original does the cover. Johhny Cash singing "Rusty Cage" by Soundgarden?
Me First and Gimme Gimmes doing "100 Miles" by the Proclaimers? Awesome. (Couldn't find a video of this one).
Matt Weddle singing "Hey Ya" by Outkast?
I don't know what it is about covers, I just like to see other takes on a piece of music. Generally, if the musician doing the cover is good at what they do, they put their own style onto it and I get to hear something that is sometimes completely different from the original, but still holds the essence of that original.
Here's the video of the Fresh Prince cover.