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Tear Jerker: Rugrats
"I Remember Melville" is easily one of the most heartbreaking episodes in the series, featuring concepts of death being explained as Chuckie goes through the loss of his pet bug, Melville. On paper it sounds like a silly idea, but the execution of the episode is nothing less than impressive.
"Spike Runs Away". Tommy and Chuckie crying over losing Spike is just sad, especially to anyone's who has ever lost a pet. Thankfully, it gets better.
While the episode was intended as Nightmare Fuel, "The Mysterious Mr. Friend" is one of the most depressing episodes in the series. This toy clown named Mr. Friend merely wants to play with Tommy and his buddies, but creeps them out unintentionally, and he doesn't know better. The poor guy ends up killed in the end.
The crying scene in the episode where Angelica thought she was going to move away.
Chuckie's reaction to the dance at the beginning of Rugrats in Paris. It doesn't help how nostalgia-inducing and saddening the song is.
It's natural to feel bad for Chuckie, but don't forget Chaz. He keeps her belongings stored away and doesn't talk about her much. It's clear that up to that point in the series he wasn't yet able to get over what happened to her. The scene where Chaz finds that Chuckie has gotten a hold of some of her stuff is downright heartbreaking.
In hindsight, many of Chaz's interactions with Chuckie come off rather poignant as a result, as it is blatant how emotionally dependent he is on him due to the loss of his wife. The fact both are AdorkableNervous Wrecks only punctuates it.
In "Together At Last," the scene where Phil thinks Spike ate Lil. He opens his mouth and says, "Lil, I'm sorry!"
The "All Growed Up" special where it shows them as preteens. The whole special has a certain air of maturity and the pressures of growing up and experiencing new things. It then culminates at the concert scene, where Tommy and Angelica duet with some big popstar over a ballad that then flashes back to the series as a whole, showing scenes from multiple episodes. The creators did, indeed, write the special as an emotional look at the series.
Acorn Nuts and Diapey Butts, the scene at the cemetery.
The movie's climatic scene involving monkeys, rain, and bananas.
Tommy: Dil wants monkeys, monkeys want their nanners. EVERYBODY GETS WHAT THEY WANT!
Tommy's Heel Realization straight afterwards as Dil starts crying, albeit for once not usual infant screaming, but genuine terrified sobbing. He drags Dil into shelter and dotes over him until he falls asleep.
While I did not shed tears, there is one scene that hit home for me as a kid. It's the plane trip in the second movie. It did not help that the first time I saw it, my mother had just died three months earlier.
Chuckie spending an entire episode trying to release his "sea monies" into the ocean, only to become heartbroken when he actually pulls it off. Knowing that they probably died ten minutes into the episode doesn't make it any less sad to hear him call out good-byes to them.
Anyone who grew up with this show and loves toys along with cute babies are bound to cry during The Curse Of Reptar's ending (All Grown Up). Basically It has a flashback at the time they were still babies and playing with Reptar. The end of the flashback has them sleeping under a tree with the Reptar doll with Tommy holding the doll and sucking his thumb. Cut flashbacks, and eventually grown-up Tommy finds the now rusty Reptar, taking it back inside to keep in his box.
"Regarding Stuie" manages a pretty impressive Mood Whiplash, ending an episode-long string of Crowning Moments of Funny with a Tear Jerker climax. In a nutshell: Stu gets a head injury that briefly lets him communicate with the babies, but also screws up his memory and makes him act like a baby. "Stuie" then spends most of the episode wearing a diaper and palling around with Tommy and the gang. At first, Tommy is thrilled to have an adult-sized baby as a friend, but it all falls apart when he realizes that even the coolest baby can never replace his dad—and he seriously believes that he'll never have his dad back. The climax has Tommy silently weeping while looking at old pictures of himself playing with his dad, with "Stuie" (who still can't acknowledge the fact that he's Tommy's father) coming in to comfort him as he realizes how much Tommy misses his "daddy".
Keep in mind "Stuie" essentially performed a Heroic Sacrifice just so Tommy could have his dad back.
If you take in the interpretation that Charlotte had a miscarriage in "Angelica's Worst Nightmare" the episode suddenly becomes this.
In the same episode, Angelica wakes up from a nightmare involving her newborn baby brother terrorizing her and her parents ignoring her. When her father goes to see her, she starts breaking down and telling her dad that she doesn't want a new sibling and to be ignored like she was in her nightmare. Her father reassures her that he and Angelica's mother will always love and care for Angelica since she is their first child and she will never ever be replaced.