REM, The Wrong Child. Sung from perspective of a child who can’t go out and play due to some illness or disability.
Oh, and another vote for “Kilkelly, Ireland.”
Al Vaiven de Mi Carreta, by lots of Cubans over the years, in this case Eliades Ochoa. About a man who works to the bone (“carreta” is “wheelbarrow,” I think) for a supervisor (“the Englishman”) and hardly earns a penny.
Also, I don’t understand much Portuguese, but the entire genre called fado sounds so sad, they must be singing about something awful.
Grateful Dead’s “Black Peter” is pretty brutal.
Marty Robbins, “They’re Hanging Me Tonight”
When a girl I was crazy about broke up with me in college, ‘Blood on the Tracks’ was my soundtrack for the post break-up moping period, especially that song. I don’t think you’ll get the full impact of the song from that link, though (no sound).
‘Brick’ by Ben Folds Five always gets to me when I hear it.
Perhaps it’s been mentioned above (not in text but some people just tossed up links with generic “here’s a real sad one” comments as description)…
Teddy Bear by Red Sovine is a trucker sharing a story about a little kid who connects with him over the CB and shares that he’s only looking to chat because he’s crippled, and his dad died.
Oops, I posted it from a machine without sound and didn’t notice, sorry for that. Here’s a working link:
Mentions of Teddy Bear and the earlier Christmas Shoes remind me of Oscar Wilde’s line about Dickens’ The Old Curiosity Shop.
Regards,
Shodan
I always thought that “Fast Car” was a sequel to Bruce Springsteen’s “Born to Run.”
That is, it tells exactly what Wendy’s life would have been like if she’d been foolish enough to run off with the young rebel in Bruce’s song.
I agree, but at least it has both a sad yet also kind of a happy ending. Nowhere near as soul-crushing as* Allegro Non Troppo* (I’m not going to add a link, if you haven’t seen it consider yourself lucky…)
Yeah, seconded. I can’t even watch that anymore (and I didn’t make it through “The Cat Carol,” either.)
“Seasons In The Sun” by Terry Jacks
Forever Autumn, from* Jeff Wayne’s Musical Version of The War of the Worlds*
ETA:
If I could change Your Mind, from The Alan Parson’s Project Eve
Al Green’s cover of “How Can You Mend a Broken Heart?” is my pick. Not so much for the song itself but for Green’s performance of it.
I researched “Danny Boy”/“Eily Dear” before I sang it as an assignment in a college voice class. The background just makes it all the sadder. 
Somebody Done Somebody Wrong Song
So please play for me a sad melody
So sad that it makes everybody cry-y-y-y
A real hurtin’ song about a love that’s gone wrong
'cause I don’t want to cry all alone
Sad only because the mere thought of that dreck makes me want to shoot myself, and I feel sad for what my loved ones would go through after my suicide.
Wishing You Were Somehow Here Again
Too many years fighting back tears.
Why can’t the past just die?
I’ll put in an nth vote for both “Kilkelly Ireland” and “Willy McBride” (AKA “The Green Fields of France” or “No Man’s Land”).
The Band Played Waltzing Matilda and Cat’s in the Cradle having alreafy been mentioned, I have to add I Will Wait For You by Connie Francis as featured on the Futurama dog episode.
That one just murders me.
And I suppose The Springhill Mining Disaster by the Dubliners et al as well.