At least, that's the one that always makes me cry.

Anything by the Magnetic Fields is also good. Grand Canyon is particularly lovely:

If I was the Grand Canyon
I'd echo everything you'd say
But I'm just me, I'm only me
and you used to love me that way

as is All My Little Words:

You are a splendid butterfly
it is your wings that make you beautiful
and I could make you fly away
but I could never make you stay
Not for all the tea in China
not if I could sing like a bird
not for all North Carolina
not for all my little words.

Hey, you didn't ask for happy love songs, right?