Elvis Costello is the King of The Depressing Song. Shipbuilding rips me to shreds, and the songs about his grandmother, Veronica and That Day is Done are very sad as well.
I’ll second John Prine’s Sam Stone, and checking those old Depressing Song threads, I’ll stand by my previous assertation that The Handsome Family’s The Woman Downstairs still has some of the most depressing lyrics I have ever heard…
Chicago is where
the woman downstairs
starved herself to death last summer.
Her boyfriend Ted
ate hot dogs and wept
with the gray rats out on the fire escape…
although pretty much anything by The Handsome Family would qualify
More folk/country than pop…but it’s hard to go wrong with Cold Missouri Waters. Written by Canadian James Keelaghan, I like the version by Cry Cry Cry
The story is based on a true account of smoke jumpers as told in Young Men and Fire.
"On Aug. 5, 1949, 16 Forest Service smoke jumpers landed at a fire in remote Mann Gulch, Mont. Within an hour, 13 were dead or irrevocably burned, caught in a “blowup”–a rare explosion of wind and flame. "
The song is told from the viewpoint of Dodge, who survived the fire by building a “ring of fire” around himself.
Actually, as the name suggests…the entire Cry, Cry Cry album is full of sad stories.
I’ll second this one. It’s the one I thought of as soon as I read the title of the OP. After hearing this song one time, I could never listen to it again. I would hit the radio button as soon as it came on, and if I was somewhere in public where it was playing, I would leave until it was over. Sure, it’s cloying and sentimental and it’s meant to have that effect, but it really drives home what it must be like to experience the loss of such a unique and delightful person who brought so much brightness and joy into your life. You just know he’ll never find that kind of person or that kind of happiness again.
Wonderful by Everclear, about a divorce, from a child’s point of view.
I love that book. I really do. Now I need to find this album.
Another folk/country song that I love I just remembered.
Leslie Fish is a rather prominent filk singer - that is she sings what are basically folk song on an SF or fantasy tilt. She’s also been doing, for several years, now, a series of albums where she records various of Kipling’s poems to music. It works out to be a very effective way to listen to Kipling, I think. My favorite one of hers in that vein is Birds of Prey March. The music is a cheerful marching tune. The lyrics are so bitter and bleak… I keep wondering why the various war protestors haven’t started trying to get this poem more well known.
I’ve also remembered a song that Trout Fishing in America covered: Prom Night in Pigtown. Another cheerful song, with a very depressing reality hovering over the celebration.
There are many in The Smiths’ catalog, but I think two win out:
There Is A Light That Never Goes Out
That Joke Isn’t Funny Anymore
I had a hard time in my first job out of college, missed home, and generally thought life sucked. I listened to Blind Melon’s Galaxie and not long after Shannon Hoon died, so that song is particularly depressing as well.
For a recent release, and an anthem for middle-age burnout, how about Childish Things, by James Mc Murtry:
Hurt - Sung by Johnny Cash.
common people by pulp . even more depressing covered by William Shatner.
also
rocketman by elton john
I was thinking of that song when I was reading this thread–in particular, this passage:
You’ll never live like common people
You’ll never do what common people do. [ LYRICS DELETED BY MODERATOR ]
It’s not only depressing but also very angry.
I never cared much for the NIN version of this song, but when I heard that cover it really tore me up. I could safely say this is probably the most depressing song I have ever listened to myself, and it’s even worse if you’re watching the video. Yet you can’t tear your eyes or ears away from it.
A good chunk of everything Pink Floyd ever did is pretty depressing, but Comfortably Numb and Wish You Were Here are the two that kill me.
Just a nitpick, this song was composed and originally recorded by Eric Bogle, an ex-pat Scotsman in Aus actually. I’ve heard many other renditions, including The Pogues, but I still reckon Boges does it best. He does “depressing” really well. Heh, some might say he’s made it into an artform. 
Check out:
A REASON FOR IT ALL
*Summer smiling on the city, it’s another lovely day in Sydney
Sunshine pouring down like honey in a golden water fall
But in the room where Claire is dying, no sunshine sends the shadows flying
[ LYRICS DELETED BY MODERATOR ]*
Back to the OP and away from Eric Bogle…anything by Dory Previn is wrist-slashingly depressing. 
John Hiatt…“She Don’t Love Nobody”, particularly the version by Nick Lowe.
its the point in the song that he realizes that the girl is slumming it with him. it hurts me
Oh, one other Tori Amos number: “Playboy Mommy.” It’s hard to write an uplifting song about having a miscarriage, and, well, the thing isn’t uplifting. She does have a little bit of a sense of humor about it, which I think only serves to make the proceedings sadder.
Being young and not having experienced (and really, not even being able to imagine experiencing) any sort of melancholy older-age retrospective, I think one of the saddest songs I’ve heard is Brand New’s “Me vs. Maradona vs. Elvis” which describes the emptiness of how women use men to feel accepted and men, knowing this, are taking advantage of it. Unlike losing a child or lamenting past regrets, I actually relate to this…
I will lie awake
and lie for fun and fake the way I hold you
let you fall for every empty word I say.
*
If I ever decide I’d like to kill myself, but I need just a little more motivation, I’d listen to Wasted Time, from the Eagles’ Hotel California album. Yeah, that ought to do it.
Not nearly as bad but still depressing: Jackson Browne’s In The Shape of a Heart.
Ooof. Yeah that one gets me too. Come to think of it, the Dead had a lot of sad songs in their repetoire.
**Wharf Rat ** always tugged at my heart strings. When I used to volunteer at a homeless shelter, I knew a lot of August Wests.
A few others that are sad,
He’s Gone
Black Throated Wind
Brokedown Palace
Black Muddy River
2 songs by Natalie Merchant need to be mentioned. The first is Eat For Two which is sung by a girl who has become pregnant after a one night stand. The second is Dust Bowl Days which is sung by a young single mother who is losing the fight to support herself and her 2 children. Both songs are sad making and the women who are singing them are very depressed. They depress me but maybe I just get depressed easily.
I submit Keep Me in Your Heart for a While, from the last album Warren Zevon recorded after announcing he was dying of lung cancer:
Shadows are falling and I’m running out of breath
Keep me in your heart for awhile
If I leave you, it doesn’t mean I love you any less
Keep me in your heart for awhile [ LYRICS DELETED BY MODERATOR ]
…
Hold me in your thoughts, take me to your dreams
Touch me as I fall into view
When the winter comes, keep the fires lit
And I will be right next to you
…