Lots of sad songs here, most of which I have not heard.
Personally I usually listen to country, which has lots of sad songs. You might say it is the foundation of the entire musical style, at least the good parts.
I will, however, confine myself to one song from each performer to keep this interesting. So in increasing order of sadness we have:
Hank Williams Sr. : I'm so lonesome I could cry
I am not a great fan of Hank Williams Sr., but no discussion of sad songs would be complete without mentioning him. This song is the one which sticks in my memory.
Johnny Cash: Sunday Morning Coming Down
Cash has been mentioned earlier, but I don't like the 'Hurt' song so much. This old one however really gives perspective to a sad and pointless existence.
and finally, the great poet of alternative country
Townes van Zandt: Marie
It might be because he suffered from depression for most of his adult life, but most of Van Zandt's songs are either sad or hopeless. This one is both.
If you have not heard it you can check the lyrics here: http://www.risa.co.uk/sla/song.php?songid=21419