Duane Allman - Goin' Down Slow

Not necessarily depressing but one of my favs by Duane . . =)

There are three I can think of right now, I'm sure there are more, I should really look into this topic later when I find the time.

I think there is nothing more depressing than listening to [url=http://en.wikipedia.org/wiki/File:Taps_on_bugle.ogg]taps[/url] on a funeral. It's usually the part where even the most steadfast break down.

Where have all the flowers gone by Pete Seeger (originally from an old folk song, if we want to be nitpicky).

The show must go on - both parts encouraging and depressing, since it was on of the last recordings Freddy Mercury made, and while he was already extremely ill.

Love Will Save You by Swans is my choice for this, since the topic got bumped. Hell, most songs with Gira involved would be up there.

http://www.youtube.com/watch?v=Tf6anhPvXoQ

Amazingly soul rending. Great vocals too.

Not sure there is a "most" depressing one, so here's a few from Poland from the top of my head.
Republika - Odchodzac
Proletaryat - Nie masz nic
Dżem - Do kolyski
Dżem - List do M

[edit]
Geez, Youtube had only one version of this song, and the quality was worse than Rick Rubin doing Norwegian black metal. Finally found it on wrzuta.pl:
Klan - Po co mi ten raj