NPR’s All Songs Considered is putting out a Breakup Song episode for Valentine’s Day and put out a call for favorite breakup songs. It piqued my interest enough for me to slap together a list.
What are some of your favorites?
“The Break Up Song (They Don’t Write 'Em)” by the Greg Kihn Band
There’s also “Between A Man And A Woman” by Kate Bush (lyrics) This is more about someone who interferes in a rocky relationship and makes things worse though.
“Your Dictionary” by XTC.
“Thank God and Greyhound She’s Gone” by Roy Clark.
Gotta love those “We broke up and I’m thrilled about it” songs.
“Feel A Whole Lot Better” by the Byrds
“Black” by Pearl Jam
“Hard to Say I’m Sorry” by Chicago
“Night in White Satin” by the Moody Blues
“Photograph” by Ringo Starr
“Don’t Think Twice, It’s All Right” by Bob Dylan
“I’m Sorry” by John Denver
“I Don’t Care Anymore” by Phil Collins
One of the best ever: “Sara,” Bob Dylan’s failed plea for his wife to come back.
Oh, and about half of Roy Orbison’s songs.
“You’re Breaking My Heart” by Harry Nilsson 
“It’s Too Late” by Derek and the Dominoes
“Nobody Knows Me” by Lyle Lovett
“Love in Vain” by Robert Johnson
“Feelin’ Alright” by Traffic
Most of the Pernice Brothers’ catalog fits here, but I’d particularly recommend “Clear Shot.”
I think most of the entire catalogue of rock and roll falls into this category.
Sail Away Sweet Sister by Queen.
There’s the “sounds mostly mellow but maybe a tad bitter, especially when you read the real title” example of “Good Riddance (Time of Your Life)” by Green Day, based on the lead singer’s real breakup with a gal moving to another country.
“You Oughta Know” by Alanis Morrissette.
“Song For The Dumped” by Ben Folds Five.
Edit: I see the Ben Folds Five song tops the OPs linked list. It’s worth mentioning twice, though.
Definitely cannot forget Salt in My Tears by Martin Briley:
Mildly NSFW Video
They’re pretty much forgotten now (if they were ever really there in the first place), but damn did I ever love Laughing In Your Face by Lillian Axe.
Interesting how much that song loses when you’re just reading the lyrics – musically, it’s so fricking happy sounding.
Fleetwood Mac’s Rumours is pretty much a breakup album.
One More Minute-- Weird Al Yankovic
Don’t Think Twice, It’s All Right-- Bob Dylan
“Go Now” – Moody Blues
“It’s Too Late” – Carole King (different song from Derek & the Dominos tune mentioned upthread)
“You Can’t Say We Never Tried” – Bluethings
“So Sad About Us” – Who
“Didn’t We” – Jimmy Webb
“Your Turn to Cry” – Dave Clark 5
“By the Time I Get to Phoenix” – Glen Campbell
“The Shadow of Your Smile” – just about everybody
Ben Folds is a serial divorcer, and he’s got some good breakup songs (oddly enough, he did not write “Song for the Dumped” - the drummer did)
Other than what you mentioned…
“Gone” by Ben Folds
“Selfless, Cold and Composed” by Ben Folds Five
“Give Judy my Notice” by Ben Folds
“Bruised” by The Bens
“Don’t Change Your Plans” by Ben Folds Five
“Fair” by Ben Folds Five
If you’re interested, lyrics can be found here
“Walk Away, Renee” by the Left Banke
“White Flag” by Dido
*Love letters, broken lockets,
dead flowers, candy boxes,
that’s what you’re left with when it’s over.
Now I wonder what went wrong,
why we didn’t get along,
nothing left but distance in your eyes.
There you go hand in hand,
leaving me alone to stand here
just another stupid chump.
Fights of spite and ugly talk,
in the end that’s what you’ve got,
so what’s the point in bothering at all.*
From Main and Broadway by Cub