Please offer better suggestions in the comments.
My personal sad, sad song -- the song I used to play when I was already sad and wanted an accompanying soundtrack for my sorrows -- is: "Fool To Cry."
UPDATE: On a nonpersonal level, I should think "Gloomy Sunday" would take first place, given its reputation for inspiring suicide.
ANOTHER UPDATE: Lots of great suggestions in the comments. Go in and add some! I thought of a long -- really long -- story song that gets me: "El Paso." I remember hearing the Grateful Dead do it, and recently I heard the brilliantly sung Marty Robbins version on the radio. Here's the cowboy's terrible end:
Something is dreadfully wrong, for I feel
A deep burning pain in my side
Though I am trying to stay in the saddle
I'm getting weary, unable to ride
But my love for Felina is strong and I rise where I've fallen
Though I am weary, I can't stop to rest
I see the white puff of smoke from the rifle
I feel the bullet go deep in my chest
From out of nowhere Felina has found me
Kissing my cheek as she kneels by my side
Cradled by two loving arms that I'll die for
One little kiss, then Felina good-bye.