This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / As Told by Ginger
The end of "Carl and Maude" when Maude died and Ginger later recounted Carl's off-screen eulogy, with her friends being concerned for Carl.
"Kiss Today Goodbye" has us view things from Dodie's POV on the waning relationship between Ginger and Darren: Darren gets Ginger isn't enthusiastic about his football playing, Ginger is sad over the lack of affection between them, and Simone has her eyes on Darren. It ends with Darren reading Dodie's letter (pleading for him to please stop hurting Ginger and end things) in the middle of the field while Ginger is standing and looking blankly in the bleachers.
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.
The look on Carl's face when he sees the noisy lit up ambulance pass the Bishop house is heartwrenching.
Jonas hardly appears in Lois's flashbacks, he probably wasn't around much during Ginger's early years and he seems unlikely to be the man his children need...ever.
Dave and Jonas' conversation: what you hear is a man who is realizing that his children and ex-wife are leaving him the way he left them and he's regretting he wasn't around enough...especially for saving his daughter's life.
"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.
Courtney revealing how lonely she is at home in "Mommie Nearest". Her Mother is off somewhere a lot, Blake hangs with Winston, and her father goes on business trips. She even had to beg her Mom to stay home with her for a change.
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.
Ginger's reaction to learning that Sasha got back together with his ex after not hearing from him for months. The heartbreak expressed in her eyes and her voice are just evocative of the talents of the animation team and Melissa Disney.
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.
Hoodsey in "The Easter Ham" and Dodie to a lesser extent; Joann decides to cut off contact between the Foutley and Bishop families after she gets sick and decides they're the source of her stress, then later Hoodsey tells Carl that he can't afford to lose his mother and cuts off contact (at least temporarily). This shows how far Joann has controlled her children, enough for them to not want to rebel against her ever. If Hoodsey said something like "I can't hang out with you Carl, my Mom would have my hide" or "I have enough drama to deal with from her" it'd be fine, but him taking his Mother's orders without so much of a question or a whimper and cutting off contact with his best friend...Joann is no My Beloved Smother, the kids stopped breathing a long time ago.
"Ten Chairs", Jonas facing the fact that only one of his children want him at the Thanksgiving dinner and then he makes a remark about Monster, their old dog. Ginger was longing for the cozy nuclear family while Carl was reminded of how he was left and/or betrayed by those he loved: Monster the dog ran away, Maude died, his Father left the family years ago, and the turkey he rescued from slaughter ruined dinner and ate up his precious disembodied eyeball.
In the Wedding special, when Courtney's family loses all their money due to Courtney's dad getting arrested, Courtney looks broken when she was crying in the bathroom. This is one of the few times when we see Courtney look very depressed.