This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Homeward Bound: The Incredible Journey
Homeward Bound: The Incredible Journey
Chance's sad little "Oh no, not this" as they watch the family leave. He already knows what it's like because he's already been abandoned.
When Peter tells Shadow to stay at the ranch, and he has to sit there and watch as they leave. And he repeats, "...Peter...wait...stay..."
Then Kate carries Sassy into the house and calls for Chance and Shadow...and Shadow is just sitting there in the sunset, looking at the spot where Peter left.
Kate comes home and discovers that her friends' pets escaped while she was supposed to be watching them. A few minutes later, she's on the phone, obviously teary, as she tries to get help from the rangers in the area and just gets told that it's very unlikely that simple pets could survive in the wild.
After the family is told that Shadow, Chance, and Sassy ran away, Peter proposes the idea of going to look for them, and Bob has to tell them that they "have to be realistic" about the possibility that they won't find them. Peter, already unhappy about Bob becoming part of the family and the changes he's put the rest of them through, lashes out at him. As a child, the viewer's probably more focused on the unhappiness the children are going through in this scene, but as they get older, they realize it couldn't have been easy for Bob either.
The point when Sassy falls into the river. The panic and desperation in her voice as she desperately tries to keep her head above water and how the dogs run to save her breaks my heart. Especially when Shadow is devastated when he fails. Their reunion is so touching.
And when the poor thing's been rescued by that kind soul that's drying her. She looks like she's been through the wringer, and she's so out of it all she does is mutter "Shadow. Chance. Shadow."
What about the little girl who was lost in the woods? All she could do is cry on how much she missed her parents. And her parents as well were in tears while searching for her.
Near the end, when Shadow has fallen in the muddy pit, is injured, and can't quite get out even with Chance and Sassy encouraging him. *sob*
Especially since Shadow was willing to give up because he feels he's too old. Just seeing him so broken after being so determined to reach Peter is just heartbreaking.
Also, he tells Chance and Sassy to leave him. Chance tries to get him to keep going like he did during the journey, and tells him that he loves him.
Chance: Look, you pushed me this far, now I'm pushing you the rest of the way. You know, back in the woods when things were really bad, I always believed we'd make it because I thought you were too stubborn to quit! And you're not going to quit, not now, not when we're this close! Now try again!
Shadow: Do you think it's easy for me to admit I can't do it? I'm too old...
Chance: That's not true! There's nothing you can't do.
Shadow: I have nothing more to give, Chance. And it's time for you to be on your own.
Shadow: ... you've learned everything you need, Chance. Now all you have to learn is how to say goodbye.
Chance: [devastated] ...I won't let you give up.
The last scene. Peter thinks that Shadow didn't make it, after Chance and Sassy come back. He turns, brokenhearted, to go back inside... and Shadow slowly limps up the hill, and then he sees his Boy... and runs to him.
Peter turns away. "He was old. It was too far. He was just too old." Shadow - old, worn-out, injured, limping Shadow - finally tops that last hill and just the emotion in his voice... "Peter." Cue wah-wahs.
Shadow: "Peter, I worried about you so!"
Homeward Bound: Lost in San Francisco
After the animals have been lost again, Jamie is beginning to cool down from his frustration with Chance's antics (and his life in general) and is feeling sorry about the way he treated Chance just before he left. As he and his family pile into a car, Jamie sees a boy and his dog playing catch in the rain.
A simple one, but definitely effective for animal lovers. Shadow has just brought a boy out of a burning building and the boy knows that his pet kitten is still inside. (Luckily, Sassy saved it.)
Boy: Tiger's in there.
Riley's past is also pretty heartbreaking, since it explains why he's so bitter and angry towards humans.
The sheer disregard the humans had for that little puppy. The kid didn't want to play with him right away, so what do they do? A. Give it time. It takes time for a child and a new pet to bond. B. Put out an ad for anyone else looking for a puppy. C. Turn the puppy in to a shelter or return him to wherever they got him. D. Abandon the poor thing on the side of the road to die.
Delilah: But the boy...he didn't seem to like Riley very much. Didn't want to hold him or play with him or anything. So they left Riley in the gutter on the coldest, rainiest night of the year.
Chance's Heroic B.S.O.D. at home, when he thinks he can no longer ever see Delilah. She comes to him and they reunite, but still..