If you're talking about songs that induce you to drink from the fount of romantic and spiritual melancholy like a bittersweet and toxic liquor, well, I got a million of 'em. But as far as songs that just flat-out make you sad, there's always been one that's done it for me sure as the sun sets at the end of every day.
Like any thinking human who professes any sort of love for popular music in any form, I love the Beatles. And they could do romantic melancholy as well as anyone (cue "Julia" and "Yesterday"). But the band's last single, "The Long and Winding Road," pulls from a well of sadness so deep that I must confess that I have a hard time listening to it. It's the sound of the last fragments of the band crumbling away; and in that fragmentation you can hear a pretty rich metaphor for the dissolution and fragmentation of anything--a human life, a relationship, your childhood, whatever. The strings and the gospel chorus interjections are supposed to suffuse it with some sense of grandeur and hope, I reckon, but it's like gilding and fancy decoration on a corpse. Which, for the Beatles, it was at the time.
This YouTube video includes lyrics, which are about as diametrically opposed to a pick-me-up as you can get. Here you go, if you can handle it.