^Yes to Nick Cave. Tindersticks, too. A Night In, Another Night In, My Oblivion... some of the saddest music I know.
I'm FB friends with a young musician who's been making some really good slowcore-ish sad music lately. He calls his 'band' (just him so far, with occasional female backing vox from friends) A Thousand Hours, named after the Cure song. He's a Cure fan, although his music doesn't have much in common with them. It's more a hybrid of Red House Painters and Cocteau Twins, hints of Low, some Breathless-ish synths, with also a touch (very small touch) of '80s coldwave. I'd post a URL, but I haven't written enough posts yet.
Since I mentioned Breathless, they're also on my sad music list. They're an English indie band who've been making music since the early '80s. Ivo tapped their singer Dominic Appleton for his second This Mortal Coil album because he thought Appleton had one of the saddest voices he'd ever heard. Their early music is a little more jagged post-punk, but still great. Even so, the reflective dreaminess was still there and has only grown with each album. My favorite is their 1991 masterpiece, Between Happiness & Heartache.