wow, there are LOADS of songs that make me sad. Sadness is just one of those things that songwriting was made to express. Far more effectively than unbridled joy, in fact (contrast how often it's the case that someone's best album is their divorce album, vs. the smugness of most songs about having kids... 'Isn't She Lovely' being the awesome exception that proves the rule...)
The song I've chosen though, is one that's utterly devastatingly sad, wrapped up as a fairly trad pop breakup ballad. Rosie Thomas' version isn't the first one I heard - Tommy Sims, one of the co-authors of it, did it on his exceptional (and completely unknown) album Peace And Love (here it is on Spotify), but that's not on Youtube, or anywhere else embeddable that I can find...
So here's Rosie's version of It Don't Matter To The Sun, that I heard a few years later... Still just as heartbreaking. It's a break-up song that instead of claiming that the entire world is about to collapse, undoes that metaphor and uses the parallels with the world not giving a shit to contrast the person's own pain. Genius songwriting, and possibly inadvisable to listen to if you're still raw from a recent break-up. Srsly.