Peter Gabriel/Tear Jerker

This former front man of Genesis has a lot of incredibly depressing songs.

"Blood of Eden", especially the Carnivale fanvid, is cover of The Magnetic Fields "The Book of Love". The song earns extra points by being pretty darn hilarious as well.
One Word: "Biko".
"Father, Son".
The quiet, ending section of "Family Snapshot".

All turned quiet. I have been here before
A lonely boy, hiding behind the front door
Friends have all gone home...there's my toy gun on the floor
Come back Mom and Dad
You're growing apart, you know that I'm growing up sad
I need some attention
I shoot into the light

"Don't Give Up" is a prime example. Sounds like a cheesy title, but the lyrics, melody and Kate Bush doing supporting vocals all make it really work. }}
- And then there's Shannon Noll and Natalie Bassingthwaighte's cover...
"My Body Is A Cage", originally by Arcade Fire, has always been a tearjerker. Peter Gabriel took it and made it a triumphant one.
- Pretty much all of Scratch My Back.
"Here Comes the Flood".
Two words: "I Grieve".
"Red Rain" as well.