This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Wild Thornberrys
"Forget Me Not", which has Eliza meeting an old elephant that her father befriended as a young man. She (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 suffocates and dies, 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 kept carrying her til he found a place they could rest safely. 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.