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 16 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.
Fern convincing her dad to spare Wilbur's life. She runs outside just as her mother is putting breakfast on the table, begging him not to Mercy Kill the runt of the litter.
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 he 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.
1973 animated film
Fern raises Wilbur from birth, bottle-feeding him and celebrating his birthdays. John can see she's getting too attached since Wilbur is a farm animal, not a pet, and tells her they need to sell Wilbur to her uncle when he's big enough. Fern protests about it because Wilbur isn't bacon; he's her friend. Then she runs outside, where she and Wilbur cry as she hugs him, knowing the inevitable is coming.
Fern and Wilbur's goodbye when the latter goes to live with the former's uncle. This is topped off with Fern running after the truck for a few seconds, before breaking down sobbing.
Unlike the book and live-action film, Wilbur finds out about his fate right before he meets Charlotte. Nevertheless, his reaction here is no less heartbreaking.
Wilbur tearing up when Fern leaves with Henry Fussy to the Ferris wheel. If that wasn't sad enough, he even sings a little bit of Fern's song, "There Must Be Something More" (which she was just humming to him, before Henry arrived) before breaking down.
Wilbur: The something more I'm feeling must be...(crying) Charlotte! She... she didn't even say "Goodbye, Wilbur". How do you like that?
Charlotte: I like it just fine.
After Wilbur wins a bronze medal, Charlotte explains why she helped him: spiders don't get to do much good other than eat bugs, so it's a meaningless life. So helping Wilbur proved she was more than a mindless spider. Wilbur solemnly says he owes Charlotte his life and would die for her if she needed it. Charlotte reassures her she knows he would. Only then does Charlotte announce she's dying in a few minutes, and there's nothing Wilbur can do about it. No wonder he starts sobbing.
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.
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.(passes away)
Wilbur's reaction when she finally passes on.
Wilbur: Charlotte? Charlotte? (realizes) CHARLOTTE! (breaks down sobbing)
The adults notice that Wilbur is crying. Fern knows what's wrong, given her solemn expression, and she goes over to wipe his tears. Zuckerman assumes he's homesick and reassures Wilbur they'll be home soon. Oh, if only you knew...
After most of Charlotte's children leave, a tearful Wilbur tries digging a hole below the fence to run away.
Sheep: What are you up to now?
Wilbur: I'm going away! I can't stand it here! This place is too full of memories! And all of Charlotte's children are gone!
Joy, Aranea, and Nellie: Hello!
Sheep: There are three little runts up there that couldn't fly away.
2003 animated sequel
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).
Wilbur: When we left the fair, Charlotte stayed behind. She knew she was dying...I never saw her again...
(Charlotte's daughters sigh sadly)
Joy: Guess our mom... was really special...
Nellie: I wish I could have met her.
Aranea: Me too.
The above dialogue is even sadder when you remember that Joy, Aranea, and Nellie didn't hatch until after Charlotte died. Not only did they never get to meet their mother, they were never even alive at the same time she was.
Seconds after Wilbur tells Nellie, Aranea, and Joy about Charlotte. Wilbur is alerted by Cardigan's distressed bleating. Turns out Cardigan is being separated with Wilbur at the fair where he gets sold. When Fern learns about this, she quickly protests (which doesn't work) her uncle's decision by telling him that Wilbur and Cardigan are best friends. Cardigan is heard bleating non-stop (sounding like a crying child) while Wilbur can only squeal back at him.
Aranea's frustration with not being able to construct a web properly.
The other lambs in Cardigan's flock bullying him for his black wool in contrast to their white wool can be hard to watch for victims who have been bullied themselves. Sure, the dialogue of it is rather cheesy, stereotypical schoolyard jeering, but it can still come across as uncomfortable to some.
Bully Lamb: Stay away from him, pa-thetic!
Sheep: Look at him, he's a disgrace to the farm!
Another Lamb: He's such a loser, with a capital L.
Cardigan: (staring sadly into a puddle to see his reflection) What's wrong with me...?
2006 live-action film
Charlotte's last words to Wilbur, as the latter is being carried back into the truck departing from the fairgrounds.
Charlotte: (whispering) Goodbye... my sweet, sweet Wilbur...
Wilbur: (solemnly) Goodbye, Charlotte. I love you.
There's also a deleted scene where the fairgrounds are being taken down as mentioned in the original book section, is also symbolic in heart-wrenching ways. The fair looks so deserted and bleak that it's quite disturbing. It doesn't help that it features the same quote directly from the novel. Coupled with Sam Shepard's narration actually sounding close to being choked up. It's not very hard to see why it was cut from the final product.
Fern and Wilbur's last night together, with her singing him a lullaby.