Tom Jones - Kiss
Leann Rymes - Purple Rain
Though neither should be called Cover versions and should be banned
Prince does a funky cover of "Play that funky music" though only at live shows.
Sheryl Crows "One of us" by Prince is cool.
Prince's When U Were Mine by Cyndi Lauper.
Probably the most well known cover song, "Nothing Compares to U" sung by Sinead O COnnor, which was penned by Prince some (rumoured) 11 years prior to her covering it.
As for bizzarre..............
Anarchy in the UK by Green Jelly, This band did a rather psychotic album many years ago, with songs such as the Three Little Pigs etc, very warped album, but Anarchy in the UK was hilarious, the title changed to Anarchy in Bedrock iirc and the ever famous lyrics changed and was totally penned about Bedrock and the Characters of The Flinstones
You Tube Link:
http://www.youtube.com/watch?v=K87HNwFikQ8