“Longview” and “Basket Case” by Green Day
“Angie Baby” by Helen Reddy is about an emotionally disturbed girl who is attacked by a local boy in her room and magically makes him disappear into her radio.
“Fast Car” by Tracy Chapman fits the bill too, I think.
ETA: Actually maybe not. “Fast Car” wasn’t pop. But “Angie Baby” was.
Alison - Elvis Costello
Don’t take me alive - Steely Dan
You could include a huge amount of Steely Dan stuff in this category.‘Home at last’ is an astonishing song, it extracts a new meaning from a story over 2000 years old.
Smile - Lili Allen - the vid for this is even darker, despite the jolly bouncy tune
My iPod shuffled this song up as I was mowing the lawn this morning; I was coming back to this thread to mention it! 
“Just Dance” by Lady Gaga. The singer’s character is drunk-and-or-drugged beyond all fuckeduppedness, to the point where she doesn’t know where her keys are, where her phone is, what club she’s in…she’s panicking about it but figures if she can just get out on the floor and dance she’ll be OK, eventually the buzz/high will wear off a little and she’ll be able to think straight.
Then Colby O’Donis’ character comes into the club, looking at all the fine ladies, and decides that Gaga is the one he wants. His line is “And there’s no reason at all why you can’t leave here with me.” Well, there is the fact that she is TOTALLY FUCKING PLOWED and probably not in a position to actually give consent…
“Ode to Billy Joe”
Mad World by Tears for Fears. The original is incongruously, but 80s-friendly, upbeat. Gary Jules gave it the proper somber mood that the lyrics require and it became the anthem of Donnie Darko. Can it get more dark than that?
The 80s were full of them, actually. Blasphemous Rumours by Depeche Mode: 16-year-old girl commits suicide by wrist-slitting; 18-year-old girl hit by car, coma, then dies; song questions the mercy of God.
I Don’t Like Mondays:
From Wikipedia:
I know that I’m in the minority, but I prefer the original version. But yeah, it’s not a very happy song.
Good work. Surprised you missed “Smooth Criminal” which is about a woman being beaten bloody in her apartment.
I think “Smooth Criminal” is a really awesome song with a great video/dance to go along with it…that is ruined by too-serious lyrics.
The OP mentioned New Order - they (and their predecessor, Joy Division) have a lot to contribute to the thread:
Love Will Tear Us Apart - about a dissolving romantic relationship
Love Vigilantes - about a soldier coming home to find that his wife was told that he was killed in action
Perfect Kiss - about a psychotic friend, possibly armed, who dies on a night out with the narrator
1963 - about a friend of the narrator who is about to commit a murder/suicide
Hey Now What You Doing - about a nerdy kid who gets into drugs/guns
These are just the ones that I am clear on. Many of their songs have a somber tone - funereal, even, especially the first New Order album, Movement, which deals a lot with the death of Ian Curtis.
Coincidentally I was listening to Kesha’s terrific song “Cannibal” when I opened this thread. It is a metaphorical reference about eating boys up and spitting them out, but some of the lyrics are really pushing it:
Your little heart goes pitter-patter
I want your liver on a platter
and
Be too sweet and you’ll be a goner
Yep! I’ll pull a Jeffrey Dahmer
(Jeffrey Dahmer being a serial killer in Wisconsin about 15 years ago, for those who don’t know)
Shawn Colvin’s “Sunny Came Home” is about a woman torching her home.
Get the kids and bring a sweater
Dry is good and wind is better
Count the years you always knew it
Strike a match, go on and do it
As I was reading about it just now, Colvin’s website calls the song a murder-ballad. According to Wiki…
I don’t know if Colvin means that the home was occupied with Sunny’s tormentor when she burns it down or if Colvin is just taking liberties with the term “murder-ballad”.
Good list of songs so far, and I just thought of another.
Poe - “Angry Johnny”
“Imagine” advocates atheism, anarchism, and communism–some people would consider that pretty dark…
In my defence, I posted at 3:10am.
10,000 Maniacs - What’s The Matter Here?
Paranoid, by Black Sabbath was a number 4 hit in Britain, and is much poppier in its sound than most of their work. I ends by advising the listeners to kill themselves.
Most of the songs on Elvis Costello’s early albums are about his impotence.