Here are a few favorites of mine:
Love Lost, Slipping Away, or Gone Terribly Wrong:
Brenda Lee's smoldering "I'm Sorry" or "Break It To Me Gently"
Whistful (no other way to describe it):
Jonathan King's "Everyone's Gone to the Moon" This is what they mean by the expression "haunting." Proof that no one does string arrangements like the Brits (used to.) The time signature makes it a little challenging (it's a 3/4) but if can waltz and you don't mind being the only couple on the dance floor. You will be rewarded.
Pure, Unadulterated Love Song:
The Casino's "Then You Can Tell Me Goodbye." Always makes me a little misty. Runner-up? Chris Isaak's cover of Elvis Presley's classic "I Can't help Falling in Love With You." Very similar to Elvis' version, but where they are oh-so-slightly different...magic.
Instrumental:
Remember these? Nothing says "Sixties" like Frank Purcell's "Our Winter Love" except maybe a draft notice or bench (front) seats in cars.
Those are my favorites. What are yours?