All those songs you're bringing up sound sad.
The best ones in my opinion are:
"I Don't Remember Christmas" from Starting Here, Starting Now
"Still Hurting"--- Last Five Years
"If You Hadn't But You Did"--- Two on the Aisle
"Wherever He Ain't"---- Mack and Mabel
ANYTHING from High Fidelity, especially "Desert Island Top 5 Breakups", "She Goes", "Number 5 With a Bullet", and DEFINITELY "Goodbye and Good Luck"
"Knowing When to Leave"--- Promises Promises
But MY favorite has always been "Single" from THE WEDDING SINGER.
"And I Am Telling You I'm Not Going" is an I-Don't-Want-To-Break-Up-With-You song. I don't see any Get-Out-Of-Here lyrics. And "Still Hurting" does not make the girl feel stronger. If you listened, she says "Maybe there's somewhere a lesson to learn," but then she goes back to saying "I'm still hurting."
"Goodbye Until Tomorrow" is sung right after the couple's first date.
"How could she just suddenly, completely disappear into thin water?" - The Little Mermaid