I've seen some great examples in this thread. And cheers to Witchfinder General for pointing out the almost completely obscure Scorpions debut record, I love "The Lonesome Crow".
But to me, the most depressing song ever is the 1974 track "Run of the Mill" by Judas Priest, off their debut Rocka Rolla. A depressing song not only has melancholy notes/arrangement, but it has depressing lyrics as well. This combination is no better displayed than in this song. Death, and growing old & lonely occupies my mind too much if I let it, so this song really is sad. Here are the lyrics:
What have you achieved now you're old
Did you fulfill ambition, do as you were told
Or are you still doing the same this year
Should I give sorrow, or turn 'round and sneer
I know that the prospects weren't all that good
But they improved, and I'd have thought that you could
Have strived for that something we all have deep inside
Not let it vanish, along with your pride
Now with the aid of your new walking stick
You hobble along through society thick
And look mesmerized by the face of it all
You keep to the gutter in case you fall
I can't go on
I can't go on
I can't go on
I can't go on
I, I, I, I...
You all should seek this out to hear what I'm talking about. It's just such a sad, sad song.