It's awesome to watch a band take someone else's song and do something amazing with it.
The most unique covers I can think of right now are by the bad plus; I've been pretty into them for the last couple of years and they are one of the coolest things happening in music right now imo. Their covers are great and their originals are equally enjoyable if not better. I'm absolutely shocked that I never see anyone mention them here. . . Partly because their drummer (David King) is very unique and an all around amazing drummer and partly because they're pretty controversial (especially in jazz circles). Anyway, here are some of their covers that I'm a big fan of. I would highly recommend checking them out if you haven't.
They have a lot of other great stuff, I just figured I'd put these up since these are their first songs I heard that really got me into them.
Cover of Aphex Twin's "Flim" (really creative drumming on this one) http://www.youtube.com/watch?v=sX_Ii...om=PL&index=63
Cover of Nirvana's "Smells Like Teen Spirit" (song starts around 3:00) http://www.youtube.com/watch?v=yEyfLM8tKhc
Cover of Black Sabbath's "Iron Man" http://www.youtube.com/watch?v=tyz5_al-Dww
What are the craziest covers you guys have heard?