let’s not forget “Heaven Knows I’m Miserable Now” (video)
another gem is “I Got Id” by Pearl Jam (video)
Spring by The John Butler Trio
The Persistence of Loss, Leaving Hope (both instrumental), and Eraser by Nine Inch Nails
Guess I’m Doing Fine by Beck
Fade to Black by Metallica
Dream Song by Ministry Girl: “Do you believe in Angels?” Demon (or whatever): “No.”
Don’t Give Up by Peter Gabriel
One of my favorites is “My Youngest Son Came Home Today.” A heart-wrenching anti-war song written by Eric Bogle, but best known as covered by Billy Bragg.
Dark On You Now by The Peanut Butter Conspiracy is the #1 most played song on my itunes/last.fm due to me listening to it OVER AND OVER AND OVER AND OVER a couple months ago when my last relationship was deteriorating. It really fits the “wallowing in your misery” description perfectly. Ironically it was she who introduced me to the band.
Court & Spark - Joni Mitchell
Lather - Jefferson Airplane
Verdi Cries - 10,000 Maniacs
the Night They Drove Old Dixie Down - the Band
Castles Made of Sand - the Jimi Hendrix Experience
I Don’t Want to Wait In Vain - Bob Marley (later covered by Annie Lennox)
Wharf Rat - the Grateful Dead
the Needle & the Damage Done - Neil Young
Untouchable Face - Ani Difranco
Silent All These Years / Tear In Your Hand - Tori Amos
Birdland - Patti Smith
Edit: Almost forgot - White Bird - It’s a Beautiful Day
When Somebody Loved Me, from Toy Story 2. It just breaks your heart. I always think of pets being left at the pound when I hear that song.
StG
Pictures of You - the Cure
Oh fuck!
Ya know, something always starts to irritate my contact lenses when I watch that scene. Never fails. Maybe I should dust more often. 
I even hate Jessie, but watching that scene still just irritates my contacts somehow… damn it. 
I have two:
“Southern Soldier Boy”. I learned that when I was 13.
“Aura Lee”. My dad taught me that. I sang it at a church youth show when I was 10.
Yeah, for my family the War never really ended. 
I blame it on my dad.
Okay, now I need to think of happy stuff.
“Heartworms” —Coil
“There’s too much blood in my alcohol…”
Goodbye, Elton John and Bernie Taupin
The Final Cut, the whole album, by Pink Floyd.
The Business of Things, The Beauty of the Rain and After All - Dar Williams
Next Time, This Time and Lover’s Cross - Jim Croce
Jokerman - Bob Dylan
Famous Blue Raincoat - Leonard Cohen
I Don’t Want to be Your Friend - Cyndi Lauper
Never Saw Blue Like That - Shawn Colvin
Margo’s Waltz and What He Doesn’t Know - Lloyd Cole
Dorothy - Alison Moyet
Another song I managed to forget is “Fallin On” by Finger Eleven. It’s about unrequited (spelling?) love, as far as I can tell. Making it perfect for wallowing in misery as we all probably have a certain someone that “got away” or isn’t going to be ours and all we can do is pity ourselves.
Nothing Else Matters is actually a happy song. It just sounds morose.
Which still qualifies it for this thread. Especially as it’s been mentioned at least three times.
Piece of my heat - Janis Joplin. I played it after every brokenhearted teenage break up
Tracks of My Tears - was that Smoky Robinson?
Bellbottom blues - Eric Clapton but the Cher version is sadder.
Boy with the sad hands Jay Clarkson
Ricki Don’t Lose That Number - Steely Dan
Sara - Fleetwood Mac
Still - Lionel Richie
Bridge Over Troubled Water- Simon and Garfunkle
After all these years, these songs still make me tear up
How about the really old songs, like Joan Baez used to sing: The Trees they do Grow High, I Never Will Marry, The Silkie, Little Matty Groves, all full of untimely death and other unpleasantries. Just the thing for a rainy afternoon.