This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Nightmare Before Christmas
Though morbidly humorous as well, it's very heartbreaking to see the children eagerly embrace their Christmas presents (and you get the impression they've been very good all year) only to have their long-awaited presents attack them.
The part following Jack being shot down, where we see all the kids crying as the police announce that they've yet to find the actual Santa Claus and Christmas will most likely be cancelled.
Jack's song after he's been shot down and landed in the graveyard. Until now, he thought he was doing the right thing, and now that he knows that he has essentially runined Christmas, and it saddens him greatly.
Even his argument with himself can be seen as this. He's confused and upset; he though what he was doing was right, but it wasn't. Not at all.
The original poem has Jack breaking down in tears when he realizes what he's done.
"Sally's Song" segment.
"Jack's Lament." One can really sympathize with Jack's boredom that's begun to turn into despair
Sally: Jack... I know how you feel.
All the denizens of Halloweentown's reactions when it appears Jack is dead. The Mayor sounds particularly broken up when announcing it over the loudspeaker, and the Wolf Man does a Howl of Sorrow while tears run down his cheeks.
Jack's cry of: "Merry Christmas to all, and to all a good night!" is strangely tear-jerking to some.
Jack's moment of despair when Sally uses the fog juice to try and stop him.
Jack: (heartbroken) There go all of my hopes, my precious plans, my glorious dreams!