+ Muse - Feeling Good
+ Kelly Osbourne - Papa Don't Preach (I like it :P)
+ Yeah Yeah Yeahs - Phenomenon (if you haven't heard it: http://www.youtube.com/watch?v=GRl0-ya5nM4
- Sorry it is an AMV)
+ Johnny Cash - Hurt
+ T.a.t.u - How Soon is Now (I like it. But then again, I have bad taste in music)
+ Scissor Sisters - Comfortably Numb (I think we might have already had that one)
+ Smashing Pumpkins - Landslide
+ Richard Cheese and the Lounge Against the Machine - Anything by him.
+ Sonic Youth - Superstar
+ Nancy Sinatra - "Bang, Bang (My Baby Shot me Down)"
+ The Animals or Santa Esmerelda - "Don't Let me be Misunderstood"
There are some Final Fantasy songs he plays in concert that I haven't been able to find. Miriah Carey's "Fantasy", Peter Gabriel's "This Modern Love", "Paris 1919", "Interview", etc. But they are hard to find. I don't think he has ever recorded them.
Also, Nirvana Unplugged has some good covers.
I don't think you should be allowed to do anything that samples another song. As good as some of them are, it opens things up to some bleh stuff.
I vote against the cover the Genesis song "Land of Confusion." - Forget who covers it.
That's all I have right now. I am sure others will pop into my head.