Here are a few picks off the top of my head, probably not THE most depressing songs, but should rank somewhere on the list
No Use For A Name - Fields of Agony (acoustic)
Staind - Black Rain
Weezer - Say it ain't so
Johnny Cash - Hurt (covering NIN)
AFI - This Time Imperfect
Silverchair - Ana's Song
Godsmack - Running Blind
Guns 'N Roses - Don't Cry
Nickelback - Someday
Radiohead - Karma Police