"Pop Life" – Elvis Costello. This is a live cover floating around the 'net. It's a great song for him to cover but in the recording I've got, his voice sounds really hoarse. Oh well.
"When Doves Cry" – Ani Di Franco and Aimee Mann. Sorry, but smoothing out the beat does nothing for this version. Prince's robot funk meets Joy Division-like starkness in the arrangement works much better. From another MP3.
"Raspberry Beret" – Hindu Love Gods (a/k/a Warren Zevon + R.E.M.). Has the requisite swagger, but I dunno.
"Kiss" – Richard Thompson. Easily the best Prince cover I've heard, it's on a bonus disc included with his new album The Old Kit Bag. I didn't know he had that kind of vocal performance in him, and the guitar playing is even wilder than I expect from this guy.