There are a lot...
The first song that comes to mind is the M*A*S*H theme, "Suicide is Painless"
I don't know the original singer, but Marilyn Manson and some others have re-made the song.
"Breath Me" Sia
"Hurt" Nine Inch Nails/Johnny Cash
"My Friend of Misery" Metallica
"Over and Out" Airborne Toxic Event
"Welcome Home (Sanitarium)" Metallica
"Where the Moss Slowly Grows" Tiger Army
"Everybody Hurts" REM
"Don't Fear the Reaper" I can't rember this artist

Hope that helps!