When the animals are gathering for Old Major's speech, Clover puts a leg around a clutch of orphaned goslings to keep them from being frightened or stepped on. She does this in a way that suggests she's probably done it many, many times before; she's not just Boxer's mother on the farm.
Benjamin's utter and complete devotion to Boxer. He's cynical and biting and doesn't stretch his neck out for anyone else; if you get yourself into trouble, you can damn well get yourself out. But because Boxer is straightforward, innocent, and has the biggest heart (literally and figuratively) of anyone on the farm, Benjamin loves him. Yeah, he might not be the brightest animal on the farm; but that likely just makes Benjamin more protective. Boxer needs someone clever, like Benjamin, to look after him. He's too honest and loyal for the old donkey to do anything but love him.
While it crosses into Tear Jerker territory, Benjamin's reaction when he sees that Boxer is being sold to a knacker. The book explicitly states that nobody on the farm has ever seen him show that level of emotion, for anything.
Mollie leaving. While it seems to just be a Ditzy, vain showpony abandoning her friends, at the end you're just happy that SOMEBODY got out before it was too late.
The Live-Action Adaptation
Jessie takes Clover's place as the universal caretaker of the farm. Even while pregnant—she gives birth shortly after the revolution—she's constantly running around trying to take care of everyone. This includes chasing down Jones' truck in an attempt to force him to come back and feed her friends.
Jessie makes her big introduction (after greeting Mollie to inform her of the meeting that night) by tackling Jones when he was abusing Boxer, blaming the poor big-hearted carthorse for the catastrophic plowing job that had resulted when he tried to plow a field while raging drunk. Moses is appalled by this, and when he confronts her she has this gorgeous line:
She's also one of the few who seems to genuinely like the sheep—as opposed to the others, who for the most part just tolerate them. She clearly thinks of them as kind of like big, fuzzy kids, but she's always friendly and upbeat with the "girls" and never talks down to them.
It's blink-and-you'll-miss-it, but at the Battle of the Cowshed Napoleon mentions that she's leading the sheep into battle. True, she's a sheepdog so it's not as if anyone else would have the job, but it's cute all the same. You can just picture her encouraging them and helping them along.
When Old Major dies and they have his funeral, Mollie brings one of her ribbons and lays it on the grave. She might never have believed in Animalism, but she respected Major just as much as anyone else.
Muriel the Goat, when all of the others have broken out of the farmyard to feed themselves, is left tethered outside in the rain. She tugs at the rope in an attempt to free herself, but fails. Later on, when she sees Jones and a group of farmers coming to chase the animals back in, she pulls the stake out of the ground and runs to warn them. It wasn't enough for her to just want to help herself; to get free, she had to want to help everyone.
When Jones first abandons the hungry animals to go drinking, Mollie whimpers quietly that she's "very hungry". There's a brief shot in which Boxer nuzzles her comfortingly.
Boxer, it should be mentioned, has been working hard in the field all day while Mollie was only driving a light cart—he's likely starving. The fact that he doesn't point this out, when snapping at Mollie would be both understandable and easily forgivable, is heartwarming in and of itself and says a lot about Boxer's character.
Boxer is clearly worried about Jessie when she goes into labor. He fusses over her like a mother hen, asking very sweetly if she's sure she'll be okay. She has to smile and tell him everything will be fine, and to go help the others, before he reluctantly leaves.
Again with Boxer: his first words when they discover the slaughterhouse and its contents are a very quiet "We must bury them all." Simple, understated—and immensely goodhearted.
At the end of the movie, Jessie reuniting with one of her puppies.