This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Charlotte's Web
Charlotte's death after the fair through natural causes, and how bittersweet it is.
In fact, this was so sad that the person who did the audiobook had to rerecord that passage of text 17 times because he kept breaking down.
The book narration adds "Nobody, of the hundreds of people that had visited the Fair, knew that a grey spider had played the most important part of all. No one was with her when she died."
A bit of insight into the life cycles of spiders makes an already tearjerking ending even more tragic. Orbweavers like Charlotte usually die after the first hard frost, but good weather and abundant food permitting, they can potentially live a few years. Charlotte, however, dies in the still-hot days of early fall. Whether you chalk this up to bad luck or a hard year of pushing herself physically, she died young.
Wilbur's life is safe and he can live out the rest of his days without a worry to be had, but without the one person who gave him all of this.
Charlotte did a hell of a lot for Wilbur. Her reasoning? Because he was her friend. She never asked for anything in return, helping him was enough to make her satisfied with her life.
Her death specifically in the 1973 adaptation. Charlotte actually uses the very last of her energy to edge herself out of sight on top of the wooden rafter, so Wilbur doesn't see her die.
Not even the 2003 sequel forgets; in said sequel, there is a scene where Wilbur is telling Charlotte's three daughters about how Charlotte died at the fair prior to the end of the 1973 adaptation (using remade animation for the flashback no less).
While the songs are haunting, there is this lyric:
Charlotte: How very special are we... for just a moment to be... part of life's eternal rhyme...
Fern convincing her dad to spare Wilbur's life.
It's not only from Fern's perspective, but also from John's perspective. He didn't want to kill Wilbur any more than his daughter was begging him not to. But since the sow couldn't feed the runt, he felt like had no choice but to kill the little piglet, as he sadly and hesitantly took out his axe, before Fern convinced him otherwise.
Fern saying goodbye to Wilbur when he goes to live with her uncle, as well as Wilbur's reaction when he's told by the sheep they plan on raising him to become dinner.
Wilbur's reaction to most of Charlotte's children leaving him after they're born.