Damien Rice has some good Heartbreak tunes, I have no idea what the fark he's talking about half the time but ,it's not because he uses Goidelic speech  or anything, I think he just writes from personal situations that only he and people close would get. It still works though.

Hallelujah - Leonard Cohen, Jeff Buckley, etc.

Nina Simone - Don't Explain

I have a ton of 'em but I'm drawin' a blank right now...

Ready to move on ?

New Orleans music

The Scabs - Freebird