Nice, you have Pain's Elanor Rigby up there already
How about:
Enjoy the Silence - Lacuna Coil
Have a Cigar - Primus
Johnny Cash - Rowboat (ya, that's a Beck song) Fuck it, any covers the man in black did are pretty out there
Stay - Cradle of Filth (indeed, it is the song of 1991 fame)
Burn in Hell - Dimmu Borgir
School's Out - GWAR
...and who could forget the System of a Down Zelda theme
Are you looking for suggestions because of the contrast of the musicians? My friend, look no further than Cream. I don't think they wrote but 1 original song (the goofiest one on the album) and everything else they played was written by downtrodden black guys 20-30 before they recorded it. They, being uptight middle class white British dudes.
Of course, look how many people Identify those songs with the 'Cover band' now