Tom Waits/Tear Jerker

About half of this innovative musician's output (when he isn't being seriously scary) can fall under this category.

"Christmas Card From a Hooker in Minneapolis" and "Georgia Lee". The album Blood Money (originally the score of a rock opera he co-wrote) contains a few pearls of melancholy, such as "Lullaby" and "The Part You Throw Away".
"Martha" is especially impressive when you listen to it and realize he wrote it at the age of 21!
The Black Rider has its moments, but the strangest one is "Lucky Day." It seems like a little ranted remembrance of a man's life. It's not to sad on its own, just melancholy and even funny at times. Then you see the play and you find out its context: the character singing it has just gone stark raving mad after accidentally murdering his bride-to-be on their wedding day, and he's being led off to hell by Pegleg the Devil. That's soul crushing.
"If I Have To Go" has made multiple grown men sniffle and cry.
His original version of "Downtown Train" is a bit sad, but the 'Everything But The Girls' version is heartbreaking.
"Never Let Go" is another one.
"Take It With Me" can always open the ocular floodgates.
- "Children's Story" is a particularly bad one -- and he doesn't even sing. It is also very, very depressing. Even worse if it's animated...
Everything on Alice that isn't Nightmare Fuel is this. Either that, or it's Table Top Joe.
That goes double for Bone Machine. "I Don't Wanna Grow Up" is a particularly poignant example, and "Dirt In The Ground" is just melancholy as all hell.
And from the new album, "Pay Me".
"Ruby's Arms," "No One Knows I'm Gone," "Lucky Day," "Flower's Grave..." The list goes on. Tom Waits' ballads will destroy your soul.
"San Diego Serenade"... Just... Just "San Diego Serenade".
"Burma Shave". Especially the long, improvised live versions that morph into "Summertime" by the end.

...so hush now, baby, dooooon't you cry, don't you cry, don't you cry...