This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Wild Thornberrys
Since Eliza rarely gets exasperated with Donnie and seems to be closer with him than with Debbie, when it does happen and Eliza loses her cool with him, it's usually heartbreaking.
"Bad Company": It's a subtle one, but Donnie seems to start crying when the marmosets pick him up and put him on top of the tower of various things from the commvee, preparing to knock it down.
"Forget Me Not", which has Eliza meeting an old elephant that her father befriended as a young man. Rebecca (the elephant) dies peacefully of natural causes at the end of the episode.
The Wild Thornberrys: The Origin of Donnie. To specify, when viewers discover that his real parents were killed by poachers, and near the end where the whole family had gotten too torn up to say anything.
The episode where Eliza and her father go hiking into the mountains. Eliza wants to explore more than just the trail, and finds her father's behavior—even if it's just them up there—highly embarrassing, so she sneaks away. She ends up too far, too high up, nearly succumbs to the altitude and cold, but wakes up in a cave, warm and safe. She thinks it's a group of Natives who saved her, but her llama friend tells her no, it was her father. Once he realized she was gone, he went right off the trail and didn't stop looking for her til he found her, and then dug them a shelter with just a shovel and bare hands. Just...such a display of fatherly love...*sniff*
"Marianne? Thank goodness you're here...come to Nigel. Oh, don't cry, sweet wife. Always remember that I love you and the children with all my heart." That he's delirious and saying this to a (displeased) little jungle mammal doesn't really diminish its emotional impact.
The movie itself had a few tear-jerking moments.
Akela the cheetah was almost completely helpless as she watched one of her cubs get taken away by a poacher. Even when she latched onto the human, it still did nothing to help her son.
The tone of absolute defeat in Eliza's voice when she reveals to the Evil Poachers that she can talk to animals. She knows that she'll lose her powers, but at that point, it was all she could do to save her sister.
Eliza feeling Parting Words Regret when her powers are taken away and the fact that the last thing she said to Darwin in his language was basically screaming at him to shut up.
Boko, the native boy whom Debbie befriended, getting knocked out by Sloan and Debbie's reaction.
The climax of the movie was pretty sad, considering that Eliza was unable to tell the herd that they were in danger. Had Eliza not remembered how to physically communicate with them, they would have run into the fence and been killed.
The song "Father and Daughter". Especially when it plays when Eliza says goodbye to her family as she's taken away to live in London. You can see it on their faces that the whole family is broken up by this.
The episode with the Galapagos tortoises, "Two's Company", had a part where the tortoises (said to be the last of their kind) were about to mate, but Eliza, thinking that one was hurting the other by biting their neck and not realizing it was normal, broke them up. Once she realizes what was really going on, she was horrified at herself, thinking that she had just wiped out a species. Fortunately, the tortoises successfully mate with each other near the end of the episode. This one's particularly painful in the aftermath of Lonesome George's death and the resulting extinction of the Pinta Island tortoise.
Sven breaking up with Debbie, she is completely heartbroken and angry because of her family's world traveling she doesn't really have the ability to date like a normal teenager.
In the series finale, Marianne and Nigel film the sad sight a mother bear chasing away her cub (due to the cub being old enough strike out its own) and it causes Marianne to break down in tears as she confesses her fears of her daughters no longer needing her after noticing how close they are now (due to Debbie being Eiza's Secret Keeper). Even when Nigel assures her that it means they will no longer fight, Marianne is still sad about the thought of losing her children as they grow up.