For me it has to be Ashoken Farewell
I Googled and found Celtic Woman and believe me not only is Mairead Nesbitt one beautiful woman she sure can play the violin
The Aquarium movement of the Carnival of the Animals by Saint Saens. Its use in the opening sequenceof Days of Heaven is particularly memorable.
The Lonesome Boatman, melody really gets going about a minute in - Today FM, Ireland’s biggest independent radio station uses it in the background as they read out the weather forecasts bless 'em. It’s usually strangely apt.
The Intermezzo from Cavalleria Rusticana - it’s one of the very few pieces of music that moves me to tears.
Also, the second movement of Piano Trio In E Flat by Schubert. Truthfully, I’m not sure if I’d have fallen in love with it quite so hard if it wasn’t for the perfect complement it gives to the beautiful scene from Barry Lyndon here, but I like to think I would.
The classic saddest tune in all the world that tends to get cited is Albinoni so enjoy that too. Alas, for me it conjures up the finale from Blackadder the third so it’s power of gloom is blunted.
ohh! I forgot the music from the end of Fahrenheit 451 by Bernard Herrmann
I saw the title of the OP and this is what I came in to post.
I’m So Lonesome I Could Cry
Somebody Done Somebody Wrong Song
These two capture the essence of loneliness
Irving Berlin’s “What’ll I Do?”, especially the version by Rupert Wainwright and his mother and aunt, Kate & Anna McGarrigle. There’s something about the solo piano or the slightly echoey acoustics that just make this incredibly poignant.
I didn’t know what Schubert piece you were talking about until you mentioned Barry Lyndon, and then I instantly knew which one it was without even looking at the YouTube clip. And I agree with you.
I’ll also vote for Chopin’s “Tristesse.” (Duh.) Also Schumann’s Traumerei, despite it being used in upmteen Looney Tunes as the stereotypical “sad” music.
Dead Can Dance’s Host of Seraphim.
“Vincent” by Don McLean chokes me up a bit nearly every time I listen to it intently.
There’s a version of “The Band Played Waltzing Matilda” by singer Priscilla Herdman that is very touching.
“Miss Sarajevo” gets to me sometimes, when I think what the lyrics are about.
The Last time by Kean really gets to me,plus Seasons in the Sun by Terry Jacks.
Also just remembered Everyones got to learn Sometime.
The last really hit me where it hurts.
“Hole in the River” from Crowded House. Was written about a family member’s suicide by drowning.
Well, I probably have about a dozen or two possible songs and pieces that could fit the bill, spanning two and a half centuries of human artistry…
…So I’ll just pick the last one I’ve added to the list “Orchestral Suite from ‘The Inner Light.’”
More like a “wistful, nostalgic” kind of haunting, rather than a “play over slow-motion montage of atrocities” kind, but we can’t all be Berber’s Adagio for Strings. 
Eva Cassidy’s version of “Over the Rainbow”.
Oh yes I forgot about that one, I much prefer The Pogues version though
Toad the Wet Sprocket’s Something’s Always Wrong is my favorite sad song.
“Danny Boy” is the one that always makes me weep.
These guys think so, too.
Gary Jules’ remake of Tears For Fears Mad World.