This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Lilo & Stitch
Lilo & Stitch
Not even fifteen minutes into the movie, Lilo's first scenes have her being rejected by the other girls (because she beat up Mertle). After hula class, she tries to make up with them and shows them her "doll", Scrump, only for them to disappear before she's even finished talking. The somber music sets in as she throws Scrump on the ground and walks away, only to come back and embrace it sadly before heading for home.
The Bed Time Story deleted scene is pretty upsetting. Lilo tells a story about a bear named Toaster, which makes Nani have a "That's Lilo" reaction, but it gets heartbreaking because he smells so bad that his only friends are rocks and fish, then a princess promises to bring him some special soap, but she lives far away and the soap hasn't arrived yet.
Lilo: He's so sorry he smells bad.
CobraBubbles seems a lot less funny when he comes to take Lilo away. Even worse is Nani's slow, horrible realization that she can't stop him, and Lilo's total incomprehension of what's going on. That and the fact that Bubbles truly seems sorry for what he has to do and does genuinely care about Lilo's well-being.
Later on, when Lilo is kidnapped by Gantu, and Jumba and Pleakley have refused to help, Nani crumples to the ground heartbroken, truly believing she'll never see her baby sister again. And just before that, she happened upon Jumba and Pleakley arresting Stitch, and asks them about her little sister. When they start playing dumb, she reaches her wits end and explodes in the most heartbreakingly-frustrated voice:
Nani:LILO! She's a little girl this big, she has black hair and brown eyes and she hangs around with that THING!
"Lost" translates into Hawaiian as "Lilo". In a way, It's almost like he's calling out for her.
It gets worse when you consider the implication that he's emulating the story in the hope that his family will come and find him, like how it ends.
Also, the conversation that ensues when Jumba finds him the next morning.
In a nutshell, the conversation is this: when Jumba beckons Stitch to come close, Stitch simply tells Jumba he's waiting. When Jumba asks for what, he looks down and sees the story of The Ugly Duckling underfoot, and is able to connect that Stitch is waiting for his family to come and find him. Jumba replies that Stitch has no family; he made Stitch. Jumba tells Stitch that no matter how hard he tries, he's built to destroy, Stitch can never belong in a family.
And this quote from Lilo as Stitch makes the decision to leave (roughly paraphrased):
Lilo: Our family is little now and we don't have many toys... but you can be a part of it. You can be our baby and we'll raise you to be good. But if you want to leave... you can. I'll remember you though. I remember everyone who leaves.
It's not even just what she says, but the matter-of-fact way she says it. This girl is 5 years old and has dealt with so much loss that it's become almost a normal occurrence to her.
The part where she sees Stitch looking at her family photo again—not because he wants to destroy it, but because he's curious. She then asks where his family is, and says she hears Stitch crying at night, and knows it's the reason he breaks things and pushes her. Stitch's tense expression as he clutches a pillow with his claws just sells it.
When Nani and Lilo sit in a hammock in the backyard; Nani is looking for a way to possibly tell Lilo goodbye without alarming her or making it seem like they'll be forever separated, but Nani can't articulate the message through all her pain and sadness. So she sings the most beautiful, depressing rendition of "Aloha 'Oe" and...
In the beginning when Nani and Lilo are making up after their fight, when Lilo says "I like you better as a sister than a mom," then starts to cry and asks, "And you like me better as a sister than a rabbit, right?" It was so perfect because it's SO what a little kid would say — not very articulate, not even making much sense, just so terrified that her sister really doesn't want her.
Any of the strong Nani and Lilo scenes (especially the backyard scene) are tearjerkers for someone with an older or younger sister
Lilo: You came back. Stitch: Nobody gets left behind.
Tears were shed during the "Aloha 'Oe" part on the night when Nani and Lilo were talking about family for what could have been the last time as Lilo was to be taken into child custody soon.
"I remember everyone who leaves."
"This is my family. I found it, all on my own. It's little, and broken, but still good. Yeah. Still good."
Pleakley is moved by this scene so much that he glumly asks if they couldn't just let Stitch stay. It's the sad tone in his voice that makes the moment.
This deleted scene, featuring the death of Pudge the fish. Thank Disney, that the suits actually veto'd the scene.
Lilo: What's wrong with you?! (Stitch looks guilty and confused.) Lilo: Pudge was part of our family! You don't let your family die! You don't EVER!
Lilo wishing on what she believes to be a falling star for a friend. The look on Nani's face as she overhears the wish says it all.
And the way she says 'It's me again.' Wishing on anything she can find for a friend is probably a common occurrence for her.
When Lilo explains what happened to her parents to Stitch: "It was rainy, and they went for a drive."
When Lilo's teacher asks her why it is so important that she bring Pudge the fish a sandwich, she says that he "controls the weather". Given that her parents died in a car crash on a stormy night, she is clearly trying to "appease" what she believes is the spirit that killed her parents so that no more of her family will die. The looks on the adults' faces when they realize that make this even more heartbreaking.
Is that what it was? It looked like they thought she was a little odd.
It could be both. They know why, and to the adult mind they know it won't help, and is probably actually harming her. But they don't say anything because they don't know how.
A scary thought: What if Lilo believing Pudge was in control of the weather was a more recent development? What if Pudge was originally nothing more than a de facto pet she'd been feeding sandwiches until then? What if the day her parents died were the one day she forgot or was too busy to feed Pudge? This could mean that she sees her parent's death as her own fault for forgetting to feed Pudge.
Then we come to understand why she reacted quite violently when Mertle called her crazy. She took it pretty personally.
Stitch's confession of being an alien is one for both him and Lilo. For Lilo, she was very forgiving of Stitch despite his shenanigans, but after nearly drowning and then having her house destroyed, and being taken away from her sister, she finally loses it and tells Stitch that he has ruined everything. After his confession, she's surprised, but then suddenly shoves him away from her and tells him to go away, not with shock, but with bitterness. For Stitch, he had honestly grew fond of Lilo and has done everything he could to protect her, but in the end, his remorseful expression after he changes back to his alien form, really hits you hard with how he knows that he has let down the girl who had adopted him and cared for him, and her shoving him and telling him to leave really hurts as well knowing that he has been abandoned by the only one who has ever genuinely loved him.
Earlier on, after Stitch has torn up the room as he does, Jumba muses that now there's nothing left for him to destroy. Since he never built Stitch for anything else, there was nothing left for him.
"What must it be like, to have nothing? Not even memories to visit, in the middle of the night..."
The climax. After malfunctioning and accidentally attacking Lilo, Stitch decides that it is too dangerous for him to live on Earth anymore and tries to escape to an uninhabited planet using Jumba's ship. Lilo ends up chasing after him with a hovercraft, and witnesses him crash into a mountain. Knowing the only way to save Stitch's life is to put him in Jumba's Fusion Chamber to recharge him, she activates the machine with Stitch inside, but he doesn't awaken. Lilo believes him to be dead and cradles his motionless body in her arms until Stitch suddenly grabs her arm, revealing that he did in fact survive.
Actually Stitch did die and Lilo's love brought him back. Makes it more sad, doesn't it?
"Stitch sorry." He says it so many times throughout the movie, but doing it right before he died... And before he says it one last time, as Lilo peers into the chamber, both hands on the glass, he reaches up and places his paw on the glass where Lilo's hand is. Possible Shout-Out to Spock's death, anyone?
The fact that it was so drawn out. They did the scene very well.
Jumba's entire story in the film is fairly sad: he finds out early on that Stitch is malfunctioning and dying, and spends the entire movie unsure if he can truly do anything to save him but tries his hardest to do so anyway. Elsewhere in the series, Jumba rarely makes it as evident that he looks at Stitch as his own child, and his pain as his attempts to save him fail is heartbreaking - when it looks like the only machine that could fix things has exploded, he just shuts down entirely. Luckily Pleakley is there to re-encourage him, but still...
"Jumba has failed family..."
During the film, Nani and Lilo have another small fight - which ends in a heartwarming way, but has this very tearjerking exchange, with Lilo being generally frustrated and Nani being increasingly agitated trying to help.
Lilo: (shouting) "You're not help! I wish Mom were here!"
Nani: "I'm doing the best I can!"
Lilo: (nastily) "Well, it's not good enough!"
Nani: (voice breaking slightly) "Don't you think I know that?"
The flashback scenes of the original movies, but then comes the real tearjerker scene. After waiting in vain for Lilo to appear at the beach like they had promised, Stitch thinks Lilo abandoned him so he grabs the tiki necklace from the fourth movie, hangs it on a tree and leaves the island on Jumba's ship. The sobbing hasn't even begun, though, because there's nothing more heartbreaking than seeing Lilo running towards the beach, finding nothing but the necklace and then hold it against her chest before screaming his name and falling to her knees, sobbing hysterically. That single scene is enough to make you sob for the rest of the day.
It didn't help that when Lilo's daughter is telling her about Stitch and Lilo just says that even if he was here that she wouldn't want or see him right now. Adds bonus points that Stitch heard everything she said. And his heartbroken face. (Sniff)