YES. Can’t believe I forgot that one on my list.
When the Adagio for Strings wants to kill itself it listens to Symphony No.3: Lento-Sostenuto Tranquillo Ma Cantabile by Gorecki.
What now my Love is great but just don’t listen to the Herb Alpert version.
Isolation - Joy Division
NYC - Interpol
Suffer Little Children - The Smiths (even worse if you’ve ever been across Saddleworth Moor, perhaps the most depressing place on earth).
Most of the album “Black Celebration” by Depeche Mode (except the last song, “But Not Tonight”). Hell a lot of early/mid DM stuff.
Most of the Smiths ouvre (sp?). As mentioned above, Unloveable and Asleep are particular standouts.
…
I just totally dated myself, didn’t I? But there you go.
I love Cohen, but I wouldn’t put any of his stuff into this category, so I’m surprised people are mentioning Hallelujia. Even in his most down stuff, there’s always a sort of undercurrent of “Ahhh, it was wonderful while it lasted, though, wasn’t it?” that saves his songs from being too total downers.
Oh my Og, yes! I was thinking of the English equivalent of the two songs I mention in the OP, this is it.
For heaven’s sake, what do I need to do to get a mod to fix the title? Kill myself? Oh, OK. As soon as I finish downloading some music…
Oh, and for the Spanish speakers in the audience, don’t forget Mecano’s “Me Cuesta Tanto Olvidarte”.
Well, yeah, so I am in my late 30s, why do you ask?
You know, there’s an entire sub-genre of metal dedicated to precisely this sort of mood and it’s aptly named Doom. Amongst my current favorites:
My Dying Bride - For My Fallen Angel (violin over synth strings, with spoken lyrics)
Saturnus - For Your Demons (similar as the above)
Shape of Despair - Angels of Distress (very heavy, dirge sort of metal)
Swallow the Sun - The Giant (exploration of various shades of sorrow)
Novembers Doom - Swallowed by the Moon (lyrics were apparently an adaptation from a letter he’d written his infant daught on the night he intended to kill himself; thoroughly depressing and beautiful)
Dark Suns - One Endless Childish Day (just truly epic and moving; I still get chills when I listen to this song)
Anathema - One Last Goodbye / Parisienne Moonlight (more of a break-up pair of songs, but extraordinarily poweful)
Anathema - Lost Control (simple, yet captures the idea perfectly)
Empyrium - Ode of Melancholy (title says it all)
Of course, there’s plenty of non-Doom that has the same sort of mood:
Antimatter - The Weight of the World (just acoustic guitar and some powerful vocals)
Virgin Black - Our Wings are Burning (goth truly at it’s finest)
Opeth - To Bid You Farewell
Nevermore - Dreaming Neon Black (not just the song, the entire album; attempting, and ultimately failing, to cope with the death of a love
Ashoken Farewell, in funeral tempo.
Egads, I forgot a classic of this genre: “Goodnight, Irene,” best done by Leadbelly.
Everything changes by Staind ,It’s not just the song but Aaron Lewis’s voice threatens to just tear your heart out.
Going-Away Party, as done by Bob Wills and especially Merle Haggard and Willie Nelson.
Yesterday ~ The Beatles
Turn the Page ~ Bob Seger
If you’re not in the mood by now, play “Honey,” by Bobby Goldsboro. You’ll do anything to make the pain stop.
About the only antidote I could suggest is playing “The K.K.K. Took My Baby Away” by the Ramones.
Top volume.
That’s exactly how I described the Cowboy Junkies to a friend, once.
I don’t know why, but I have the same reaction to Coltrane’s “Alabama”, as well.
(figuratively speaking, of course)
Who Wants to Live Forever–by Queen or Seal or anyone else–I’ve got a version by a female Irish singer (can’t think who) that’s…well, wrist-cutting material.
Mozart’s Requiem.
Chopin’s Tristess.
That Hallelujah song…anyone’s version…not so much wrist-slitting as much as guaranteed tear-jerker.
Also, my friends have told me that my favorite band, Frog Eyes, makes them want to gouge their brains out with a spoon. Might not be how you’re looking to go, but it might help you along 
Frog Eyes - Idle Songs
http://www.youtube.com/watch?v=I1yORDkfjok
The sorrow of “Alone Again, Naturally” by Gilbert O’Sullivan often gets overlooked because it’s not sung as a dirge. But it’s got some of the bleakest lyrics ever sung.
Also covered by Sisters of Mercy.
Weren’t the Cowboy Junkies influenced by Townes Van Zandt? I heard him perform his first “serious” song–“Waitin’ Round to Die”–at Sand Mountain Coffee House back in 1967. Pretty bleak.
The Van Zandt songbook contained lots of grim tunes but he maintained a sense of humor. His favorite introduction of one of the downers? “This is a song about living in Pasadena & commuting to Beaumont.” A concept which would make any Gulf Coaster wince…