My vote is for that tune Ramblin’ Jack Elliott just refers to as The Dog. Other people call it Old Shep.
This song was written in 1933 by Red Foley and Arthur Willis. It was recorded many times, including at least three times by Foley himself. Here’s Red Foley.
So what’s the saddest song you know?
27th Street 
A song that had little impact on me as a child but was pretty damn sad as a father: Puff the Magic Dragon.
If you really want to head south, try Drifting by 4 Non Blondes. A real bummer.
The cello is a dead give-away that something sad is going on.
I can’t listen to these! Memories of being traumatized by Old Yeller are crashing down on me.
The Ramblin’ Jack version is well worth a listen Barb. It will help you overcome Old Yeller trauma, no problem. I should say though that I like just about anything Ramblin’ Jack sings. That guy really squeezes every drop out of a song.
not sure this counts but for my money Strange Fruit as done by Nina Simone
nice choice, ink
Oh, sad 😦
My first thought was “the Magdalene Laundries” as sung by Joni Mitchell: http://www.youtube.com/watch?v=dwgTSC-stIM
But “Old Shep” might trump it.
Also up there is “Waitin’ Around to Die” and “Marie” by Townes van Zandt