Stop Your Crying - Spiritualized
It's odd, because it's a plea to someone loved to stop crying, but it's so sad itself. I love the line "I feel so broke inside but I'll devote my life to loving you"
Broken Heart > Stop Your Crying.
And as for saddest good songs;
The Weatherthans - Everything but Aside off of Left and Leaving
Deathcab for Cutie - Styrofoam Plates
R.E.M. - Everybody Hurts
Our Lady Peace - 4am
Yoko Kano - Space Lion(off of Cowboy Bebop soundtracks), and pretty much every flashback/Julia music from the series.
Blink 182 - Adams Song, I regret nothing!
Bright Eyes and Badly Drawn Boy - Cant name an specific songs but im sure theres a few sad songs, but all the songs are great.
Hayden - Most of his shit is really heartfelt and awesome
Hollies - He Ain't Heavy He's My Brother, makes me cry everytime, if only on the inside. If your Canadian and had the pleasure of the anti-drug commercial scored by it, then you would understand.
Radiohead - Fake Plastic Trees
I am sure theres like tonnes more in my playlist but I'll leave those for you atm.
*edit*
I didnt read any previous posts until after my post. Anyway, I stand by Adam's Song. And Skibas Clavicle rose like 30 points in the hot awesome meter for listing Hayden.