Jonathan Coulton/Tear Jerker

"I'm Your Moon," described elsewhere on this very Wiki as "the most touching song about astronomical taxonomy ever written." Yes, it's quite literally about Charon trying to cheer Pluto up after being demoted to dwarf planet. But really, it's hard NOT tear up at the gentle sweetness of it. "From out here, it's the rest of the world that looks so small..."
- In his series of blog posts about the fifth-year anniversary of his Thing a Week project, he noted how a song he'd only given a little bit of thought to had exploded beyond its boundaries. Although he wrote the song about Pluto and Charon, the ways in which people had been using it--as a song at their weddings, as a lullaby for their children--had made it into so much more. And he thinks that's awesome. So he's acknowledged its power himself, and just knowing how much the song has struck a chord with people is tear jerker in itself!
He is better known for awesomely geeky songs, but When You Go is a very simple song about love and loss. Set to a memorial video for a fan's pet hedgehog, it's so sad and sweet.
Then there is Big Bad World One.
"When You Go" can really affect those who have either lost loved ones, or have loved ones that are on the brink of death.
"I Crush Everything". "This one's about a self-loathing giant squid." Sounds hilarious, don't it? Wrong.
"You Ruined Everything." The title makes it sound like a particularly bitter break-up song. The actual lyrics?

"You should know
How great things were before you
Even so, they're better still today
I can't think of who I was before
You ruined everything
In the nicest way."

"Space Doggity." Ignore the funny title (It's a homage to Space Oddity, obviously) this song is so depressing it's unbelievable. It's about Laika, the dog the Russians put in space and her last moments - and it's hard not to break down in tears. It hurts because it loves. What makes it worse is the third to last verse, where the scientists back home discuss the failure of the mission.

"It's a shame
There is always something that gets compromised."

- Although, it may be more heartbreaking in the verses sung from Laika's point of view, alone and dying in space. "I don't think I want to be a good dog anymore." *sniffle*
"Womb With A View," a very gentle, almost bittersweet song about two "artificial wombmates" culminating in one being born into the world and wondering if the bond they've shared will last.

"Maybe when we get outside, we'll both still remember
Maybe someday we will meet on the street, and I'll know it's you..."

From his newest album Artificial Heart we have Nobody Loves You Like Me.
Blue Sunny Day. A lovelorn, death-seeking vampire experiences a brief, shining moment of happiness before daylight brings him down. Plenty of Lyrical Dissonance between the jaunty, bouncy music and the subject matter.
Today With Your Wife is a very melancholy song about a man spending the day with his (presumably) dead friend's wife.
- Not necessarily friend; the song can equally easily be interpreted as being sung by the man she's now seeing... which just makes it even sadder.