This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Baby-Sitters Club
A lot of Abby's autobiography.
Mimi, Claudia's adored grandmother and the one family member who really seems to understand her, has a stroke and gradually deteriorates through several books until her death in Claudia and the Sad Good-Bye.
The death of Louie, Kristy's beloved collie, is particularly bad because he doesn't simply die of old age. He had to be put down. Readers went through several books seeing Louie as an energetic, happy, beloved family pet and see him slowly become weak and sick to the point where the Thomas-Brewers admitted that they basically had to put him to sleep, because they couldn't bear for Louie to be in such pain. There's tons of little moments throughout, too, like David Michael trying to keep a half-blind Louie from going down stairs and getting hit in the eye for his trouble, David Michael opting to sleep downstairs with Louie during his last night home, the funeral...
The funeral itself has Shannon Kilbourne crying, even though earlier in the book she'd mocked Louie for not being as clean and pretty as her dog Astrid or Amanda Delaney's cat Priscilla. She even tells Kristy how sorry she is and how she'd feel just as awful if something happened to Astrid.
Speaking of Mary Anne, her mother died when she was so young that she has no memory of the woman at all. Over the years she's had to contend with several Mother's Day projects, her father's overprotectiveness, and her relationship with Logan, all without the guidance of a mother. She attempts to be a very good girl, she loses a (non-BSC) friend to a freak accident, she can be the butt of some jokes due to her meek nature, and her house burns down. She also loses Mimi, Claudia's grandmother, who functioned as something of a maternal figure for her during her childhood.
She even later finds out there was some contention between her father and maternal grandmother, which produced two more Woobies — the father who lost his young wife and is trying anything to avoid losing his daughter and the grandmother who fears losing her grandchild after the loss of her daughter and later her husband.
Not to mention that she starts going to therapy in later books and it's strongly implied that she's depressed.
Jessi's baby brother, Squirt, getting hurt in a car wreck.
Stacey having to choose between living with her mother or father. She knows one of them will be hurt either way.
There's a strong Parents as People moment in Stacey's Emergency when her parents, who are in the midst of their very acrimonious divorce, bicker in her hospital room over whose fault it really is that she's taken such a turn for the worse. She yells at them to stop it, and instead of this causing them to realize that they're both to blame, they instead turn on her. Anyone who has ever been ill, especially chronically ill, and had their situation made worse by unrelated circumstances will immediately sympathize with Stacey — especially as there's never an apology from Mom or Dad.
Kristy's breakdown after it's revealed in The Truth About Stacey that the Babysitters Agency deliberately sabotaged the BSC by sending two lackeys to skip out on sitting jobs, which made the BSC look bad. Kristy's in tears, sobbing about how she's always tried to just do the best job she can and she's heartbroken that someone would be that malicious for no real reason.
There's something about the series' conclusion that hits hard: as cheesy, unrealistic and downright irritating as the books could be at times, waving goodbye to these characters feels like leaving old friends behind. Or maybe that's just the nostalgia value.
Nate and Joey from Claudia and the Terrible Truth, who are undergoing their dad's abuse when Claudia starts sitting for them. Claudia observes evidence of both verbal and physical abuse, but fortunately is able to get the boys help through her mom; Nate and Joey's mom then leaves with her kids.
Victoria from Mary Anne and the Little Princess. She comes off as snobby but is really lonely because her parents are never around due to their jobs at the U.N. and royal status. Mary Anne helps Victoria confront this and she gets better.
Jenny Prezzioso is a Bratty Half-Pint extraordinaire, but you have to feel sorry for her considering all the attention her parents lavish on Jenny's baby sister Andrea. In Mary Anne and Miss Priss, this is carried to the point that Mrs. P was ignoring Jenny in favor of baby Andrea's modeling career, and Jenny felt the only way to get attention was to try modeling, too. Double Tear Jerker because the gambit didn't work.
Danielle, the little girl with cancer in Jessi's Wish.The fact that the book ends with her going back into the hospital doesn't help.
In Dawn and Whitney, Friends Forever, readers meet Whitney, a twelve-year-old girl with Down Syndrome. She and Dawn become friends, but Whitney breaks down in angry tears when she realizes that her parents hired, and pay, Dawn to babysit her.
In Kristy and the Worst Kid Ever, the Papadakises take in Lou, an extremely angry and rebellious foster child. It's revealed over the course of the book that she's devastated at losing her birth family (her mother abandoned her, and Lou was subsequently separated from her beloved brother, who has also been taken into foster care) and is constantly tense and unsettled because she's been sent from one foster home to another.
Lou pops up again in Abby and the Best Kid Ever. As the title indicates, this time she is well-behaved, to the point that it seems overdone and forced. Abby eventually finds out that Lou is terrified her new foster parents will send her away if she makes any mistakes.
During Aloha, Baby-Sitters, Claudia's entire arc is a Tear Jerker. During a trip to Pearl Harbor, Claudia struggles with her identity as a Japanese-American, and the fact that the Japanese were America's enemies in World War II. She even assumes a veteran she meets will hate her. He doesn't; as a matter of fact, he's the one who makes her feel better about being Japanese.
A subplot taking place over several books was Claudia's aunt Peaches trying for a baby. After several failed attempts, she finally gets pregnant — only to lose the much longed-for baby. This was eventually happily resolved with Peaches having a healthy baby.
The whole of Mary Anne and the Memory Garden, in which Mary Anne's friend from school is killed by a drunk driver. Mary Anne is overcome with grief, and even Kristy has a Heroic B.S.O.D. for a little while.
The Little Sister series has its share of these moments:
The death of Karen's step-granddad (Seth's father) in book #70. He'd had a heart attack 5 books previously, but even though he recovered he wasn't quite the same physically. He suffers another heart attack while living with Karen's little-house family, but this time he doesn't make it. The crowner, though, may be when Granny goes back to her farm in Nebraska all alone.
Two books later, Midgie the dog runs away and goes missing for weeks. She comes home at the end, but while she's missing Karen notes that it hasn't been that long since Granddad died and Seth is still stinging from the loss.
The death of Boo-Boo in book #103. The previous book had addressed his aging and the family getting a new kitten, but his health declines and he loses weight until one day he takes a nap in the linen closet and dies peacefully in his sleep. Even though he's old, it's still a big loss for the family since he'd been around for a long time. Watson had had him since he was a tiny kitten.
Books #95 and #96 have Karen deciding whether or not to join the little-house family in Chicago for six months, and Andrew begging her to come with him and to promise they won't be separated. Karen initially keeps her promise, but gets homesick after being in Chicago for less than a week. It's painful for both her and Andrew when she tells him she wants to go home; Andrew cries, and Karen feels bad for breaking her promise.