Best songs played by non-author artists...

Let's have an interesting talk about artists that creatively perform songs that had been performed by different original band or artist. There is a huge number of singers, artists that perform songs that they didn't write neither music or lyrics and they do it very often way different from the original performers and that's exactly what I really like because each artist should have his own signature without repeating after anyone else. I would not be surprised that there are people that only love the original performance, but I welcome and greet anybody who can perform let's say Pink Floyd in his own way...
If possible, share tubes as well!
Here's what comes into my mind:

Jail House Rock by Residents: http://www.youtube.com/watch?v=7zwmt7hdaHw
My Way by Nina Hagen:
http://www.youtube.com/watch?v=Q22N1dSXiN0
Man's World by Residents:
http://www.youtube.com/watch?v=TAYCeHE-Ih0
Ring of Fire by Frank Zappa:
http://www.youtube.com/watch?v=hTmTobf9KSY
Frank Zappa also made quite a few funny parodies of Stairway to Heaven, Purple Haze and other songs of famous rock, country and jazz artists.