I could probably come up with sadder songs, but this one came up on my iPod last week and it knocked the wind out of me.
The Man in the Bed – Dave Alvin
“I Dreamed a Dream” from Les Misérables.
“500 Miles from Home”–the guy really misses his family… 
“I Am a Rock” by Simon & Garfunkel; at the end:
And a rock feels no pain
And an island never cries
“Bird in a Gilded Cage.” (The composer went to a brothel to write it. It made the prostitutes cry. The composer commented, “If my song makes THEM cry I have a hit on my hands.”)
Just about anything by Tammy Wynette
Alwayshaunting.
Fast Car by Tracy Chapman. A girl starts out enabling a drunk father, and escapes to a better life, which turns out to be enabling a drunk husband, raising their kids in poverty-level existence. No hope for a better future, and her kids will probably end up like their parents.
StG
Why, Baseball’s Sad Lexicon, of course:
Says so, right in the opening line. 
In “Lineup for Yesterday,” Ogden Nash included these lines:
E is for Evers,
His jaw in advance;
Never afraid
To Tinker with Chance.
Alone Again by Gilbert O’Sullivan. The peppy music conceals how bleak the lyrics are. But if you listen the singer is telling about how terrible his life is and he’s too depressed to even commit suicide.
Spanish Doll by Poe
Mike & The Mechanics The Living Years. It came out right when my father died, and still breaks me up pretty badly. Can’t even see through the tears while I type.
http://www.lyricsfreak.com/m/mike+the+mechanics/the+living+years_20093565.htmlI was about to post that! It’s one of the saddest songs I know, along with The Green Fields of France.
That’s a cover of a 1964 hit by J. Frank Wilson and the Cavaliers, for what it’s worth.
Michael McDonald, I Can Let Go Now.
Heartbreak, plain and simple. Everytime I play this I have to immediately play something upbeat to clear the sadness from the room.
“One Last Goodbye” by Anathema
I’m at work, so I can’t provide a link, but I don’t think I’ve ever heard a song that more perfectly captures grief. Three of the members are brothers, as as I understand, the song is their tribute to losing her to cancer. What makes it especially powerful is just how simple it is, the crescendo, and the sort of lyrics that very much mimic the words that go through my head when I’ve been in that kind of grief. It’s even more powerful as perhaps the centerpiece of a concept album that explores these concepts, and the song that follows. Regardless, Anathema is one of those bands I cannot highly recommend enough for anyone who even remotely likes prog rock; hell, even people I know who generally detest the genre have loved them. Go listen to it.
I Can’t Make You Love Me by Bonnie Raitt.
Great song, but what a downer. “You can’t make your heart feel something it won’t”
Whenever I hear this song, I want to contact Bonnie and tell her she’s not homely at all. (white lie)
That is rather melancholy, but at least it’s alleviated by the songs that come after it-- “Move On” and the “Sunday” reprise.
(The one line that always chokes me up is the last line of “Sunday”…“on an ordinary Sunday.” Because it WAS just an ordinary Sunday…and this artist made it extraordinary. That’s the wonder of art.)
Came in to mention Keep Me In Your Heart and was beat to it. I can’t even listen to it, it make me choke up.
Wharf Rat by The Grateful Dead.
I’m Still Here by Tom Waits off his Alice album
