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Tear Jerker: As Told by Ginger
The entirety of the episode "A Lesson in Tightropes," which has Ginger needing an emergency appendectomy after Darren breaks up with her. The song "Splinter in my Heart" combined with Ginger's surgery, her mother looking back at her life, and a shot of the mantle in their house with photos of the Foutley family including a small candid shot of Jonas (Ginger's biological father), are a perfect example of this trope.
"Hello, Stranger" has Ginger reciting a poem she wrote for her father who never showed up to hear it read. The episode was nominated for an Emmy Award for a reason.
Especially this line;
Ginger: "And, Mom? ...Thanks for the flowers."note Lois had sent Ginger flowers after the show with a card signed from her father, trying to fool her into thinking they were from him
Another of Ginger's poems, "And She Was Gone," and the accompanying episode with the people around her thinking that the poem is a warning sign for suicide.
And it was a not unreasonable mistake on their part for people to assume Ginger was suicidal. The girl had been through a lot over the past year, and her parents are divorced.
On the flip side of that, seeing how quick people were to assume Ginger was suicidal and how differently people treated her when she only wrote the poem on a whim can hit really hard if you've been in similar situations.
Let's not forget the puppet girl who we see in the real world several times as a homeless girl freezing in the cold who disappears with the wind, leaving only crows in her wake. It's quite heartrending to see her suffering in the cold, and it's heavily implied that she's been dead all along. That combined with the previous points makes for one heck of a depressing episode.
In only the second episode of the series, "Carl and Maude," Carl befriends and falls for an elderly woman named Maude. He invites her to dinner and plans to propose to her. She dies during dinner.
The strain of Ginger, Dodie, and Macie's friendship over their different levels of maturity in "Come Back, Little Seal Girl."
"An Even Steven Holiday Special" with Jonas visiting his family.
Ginger overhearing the phone conversation between Mipsy, Miranda, Dodie and Macie to break her and Darren up in "Wicked Game" coupled with the end of the episode where Dodie tries to call Ginger and instead leaves a tearful apology message on her answering machine.
All this time and no mention of the last minute of "No Hope for Courtney"? With the principal announcing to Carl's class of the passing of Mrs. Gordon.
And the memory dedicating Kathleen Freeman's passing. Happening before the episode was finished.
One episode had Macie's parents forget her birthday. Her phone call with her friends is just heartbreaking.
Dodie: What kind of parents forget their own kid's birthday?
Macie: As it turns outů Mine. (Hangs up and curls up into the fetal position while crying.)
In one of the few moments where Miranda has ever shown a conscience, during the Summer of Camp Caprice special, Darren shows her a letter from Ginger who says that Courtney is having a terrible time at Camp Caprice, is all alone, and hasn't managed to make a single friend. Instead of savoring the fact that Courtney is miserable because by going to Camp Caprice Miranda wasn't allowed to vacation with the Griplings and had to go to her dad's military camp, Miranda starts crying and blames herself. She says if she hadn't pushed Courtney into wanting to prove she could survive at Camp Caprice this wouldn't be happening.
Most of "Losing Nana Bishop", wherein the kids react to the death of Dodie's grandmother. The death in the family is sad enough, but Hoodsie's subplot is what really cinches it. His mother ends up asking him to deliver the big eulogy speech at the funeral, which forces Hoodsie to confront the fact that his grandmother always showed more affection to Dodie than she did to him—a fact that most of his family is oblivious to. The fact that he still manages to deliver a heartfelt tribute to his grandmother, despite not having any of Dodie's rosy memories of bonding with her, really speaks volumes about the kind of person Hoodsie is. If you never wanted to give Hoodsie a big hug before that point, that episode will do the trick.
The majority of "Ms. Foutley's Boys", where Lois briefly dates Buzz the plumber, is played for laughs, but the ending is fairly sad. Not for Lois, mind you, but for Carl. Before Lois marries Dave the doctor, that episode is one of the few times that Carl briefly has a father figure who he can actually relate to, and he really seems to get his hopes up that Buzz will end up staying with the family. Even though he clearly wants his mother to be happy, it's hard not to feel for Carl at the end, when he has to go back to being the only man in the Foutley house once again.