"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.
"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".
And "Back in the Crowd," a heartbreaking plea for an ex-lover to go back to seeing him as just another stranger rather than condemning him to the melancholy yearning of being Just Friends when they've been so much more to one another.
"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...
"Come On Up To The House", which almost perfectly describes the feeling of depression.
"Hell Broke Luce" is one when you realise that it's based on the story of a real soldier, Jeff Lucey, who killed himself after returning home from going to war.