It sometimes cool to hear a song from one genre covered by an artist in a completely different genre. I recently saw Gov't Mule and they did Prince's "When Doves Cry" and it was phenomenal. It didn't really sound like Prince's version but I thought hearing their particular take on the song was pretty cool.
I guess the thing that makes that difficult to pull off is the potential for the covering artist to lose some cred in their particular milieu (you know, I think this is the first time in my life I've actually used that word.

). But assuming that fans would be open minded about it, how about something like :
- Megadeth doing Debbie Gibson's "Shake Your Love"
- Taylor Swift doing Joan Jett's "Bad Reputation", or better still, The Runaways "Cherry Bomb"
- Bootsy Collins doing "Rock and Roll All Night"
- Ted Nugent (Mr. hardcore right winger) doing a song from a hippie band, perhaps the Grateful Dead
But to be a little more serious, how about Iron Maiden doing a Queen song? Bruce Dickerson has an amazing voice that I'm sure could do justice to some of Freddie Mercury's best work. I never thought about that one before, but I thought a good way to do it would be to come up with two bands with singers who have big, unique voices and those two popped into my head.