This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Fruits Basket
The last TV episode, and also the part with Momiji talking about his mother, which they later topped with his sister Momo — whose plea to get to know Momiji even made Tohru bawl. Hatori's backstory has also managed this on many people.
Hatori wiping Kana and Momiji's mother's memory.
The tears cried over Hatori's flashback in episode 8 of the anime completely sold Fruits Basket as a quality series.
And what makes it even more heartrending is the instrumental version of the opening theme song playing in the background.
Then there's the Fridge Horror of the effects of Akito mind raping Kana. Allegedly, after the ordeal, she spent all of her time sobbing and blaming herself for Hatori's eye injury, no matter what Hatori or Mayu said to her. Don't get it yet? Kana was driven to clinical depression.
When Tohru sat by her mother in the hospital. Of course, this scene shortly flashed during Momiji's painful flashback.
Katsuya's death. Got even worse when all his relatives started badmouthing Kyoko.
Then we have Kyoko plowing through the Despair Event Horizon after Katsuya's death, seriously thinking of killing herself... and when she's about to throw herself into the sea, she sees a mom and her kid, and remembers that Tohru is still at home. And when she returns, it turns out little!Tohru was waiting for her return, innocently unaware of what had been going on Kyoko's heart. M-my heart.
And especially in retrospect, when you realize just how extraordinarily unfair the Cat's lot has been since then.
When Momiji's father tells him he has to stop violin lessons because Momo wants to learn and they can't risk the two meeting. It's possible that that's the moment when Momiji finally gives up. You said you would still love me as much as ever, but you know what? You've chosen her over me every single time you had to make that choice. And I'm done with this.
And then when his curse breaks... More specifically, when Kyou confronts him about it and Momiji turns back to look at him, all hunched over, with that tortured smile on his face...
Yuki's flashback to his childhood, late in the series. It's terrible to see his childish confusion turn to dismay, then despair, as he realizes just how alone he is. Everyone he reaches out to rejects him, with apathy or anger or cruelty. No wonder he was so reserved at the start of the series.
Akito beating up Momiji during the first beach chapters. He does his best to protect Tohru, but Akito gets angry and starts punching him. Once Akito leaves with Kureno, Momiji starts crying. Tohru immediately runs up to him and hugs him, trying to comfort the poor boy.
"I have no redeeming features." Girl needs a hug.
Nobody's going to mention Rin's backstory? That tugged my heartstrings just as much as Momiji's story.
To specify, Rin had a happy childhood, but noticed that her mother and father never seemed upset about anything. She innocently asked why that was, since she knew that most people had something that made them sad or angry. Even though she was just asking as a curious child, her parents break down and scream at her to "give [them] a break", at which point she learns that they never loved her and only pretended to. This marks the start of Rin seriously repressing her emotions, which lasts for most of her life, as she believes that if she's good and quiet, her parents will go back to being the way they used to be. Of course, all this does lead to her being an emotional trainwreck as a teenager, with the added "bonus" of everyone thinking that she's simply cold and unfeeling. This is not the case, of course. She actually feels sorry for innocent people, and very much wants to see them go on living innocently. But it's impossible for her to express this sentiment, because of how messed up she is. She also becomes an Ill Girl who eventually needs to be hospitalized, at which point her mother informs her that she can live elsewhere, because Rin's own parents have no idea how to love her anymore. Then she starts dating Haru, who is basically the only person to ever make her feel wanted or needed, only to find out that they were caught by Akito. She lies that she started it all, and is shoved out a window for that (but not before Akito takes time to tell her how useless and unneeded she is). This leads to her distancing herself from Haru, even trying to convince him she no longer loves him, and trying find a way to break the curse. She gets so desperate to do this that she offers herself to Shigure for whatever he wants (implicitly sex) if he tells her and eventually runs herself so ragged that she has an emotional breakdown, gets sick, and starts going to such lengths that Hiro actually believes she'll die if she keeps it up. To top the whole thing off, she finally finds Akito's mother, who promises to tell her how to break the curse if Rin steals a box from Akito's room. When Rin tries to do this, Akito locks her up with the threat of gouging out Haru's eyes if she escapes, at which point Rin basically gives up and stops eating. Oh, and Ren had no clue how to break the curse, and laughed about how useless Rin has always been. The girl deserves many, many hugs!
What about Kyo's backstory?! His mother's suicide and her constant worrying about Kyo and his curse leading to it. And then not to mention how his father blames and hates Kyo for it.
Kyo:(speaking about his mother's suicide.) Are you saying it's my fault?
Kyo's Father: Yes, that's right! You better admit that you killed your mother!
How about this?
Kyo's Father: You've ruined my life! All because Kyo's mother brought you into this world! Because you were born!
How about when the Zodiac curse breaks? They're all crying, and the narration combined with those images... complete bawlfest.
Oh God yes, especially as Akito looks on, monologuing about how scared and lonely she feels about facing the future. She's going through the thing she's most afraid of, and she just wants someone to let her cry and hug her.
Uotani's backstory. Her mother left her family, her father became an alcoholic, and feeling completely abandoned, Uotani joined a gang. Only when she met Tohru and Kyoko she managed to get better.
As if that wasn't sad enough, later when Uotani gets rejected by Kureno.
Machi's backstory. I can relate to it so well. She was pushed to perfection to the point that she barely managed to develop a life or any interests of her own.
Seconded so much. Takaya makes some of the most relatable characters I've ever seen in anything, despite it being a story about a family that turns into animals when they get hugged.
The entirety of Chapter 121, and 122 after that. Kyo tells Tohru about how he feels responsible for her mother's death, about his Mother's suicide, about the hat incident and how he felt when he first met Tohru. Then Tohru runs off, feeling rejected. As if all of that weren't bad enough, Tohru runs into Akito, Tohru finally understands why Akito is the way she is, tries to befriend her, and then is pushed away by Akito. As if that weren't horrid enough, when it seems that Akito may be this close to think of her offer again and accept her offer... Tohru then falls off the cliff where the series started and nearly dies.
Even though Tohru lost her mother and her dad at a young age and was left alone she decided to live on her own in a tent so as to not burden others and manages to have hope. THAT alone is a tearjerker.
And let's not forget chapter 122 of the manga, which is this from the beginning to the end. Right after Tohru's biggest CMOA aka witnessing and withstanding Akito's Villainous Breakdown... she falls off a cliff. When she was telling Akito "You Are Not Alone" and offering her friendship. Not only that seals Akito's Heel–Face Turn (with her actually screaming for help for Tohru instead of gloating, and then collapsing in tears in Shigure's arms, but it's followed by Kyo's own Anguished Declaration of Love as Tohru lays injured on the ground, a briefly conscious Tohru telling him not to cry and grieve... and at the end, their sort-of "first kiss." This might be one of the most powerful chapters in shoujo manga in years, period.
When Kyoko comes home after contemplating suicide, and finds Tohru waiting for her, just like Katsuya. What really makes it tragic, though, is that Tohru was imitating Katsuya on purpose, because she wanted to help her mom out of her debilitating depression and didn't know what else to do. She wasn't nearly as oblivious as Kyoko thought.
Kyo's whole relationship with Kyoko. She was like a mother figure to him and that whole relationship went sour just when he was a child. Then it went even worse when he was there at her death and believed it was his fault. Those two were great friends and could have had a wonderful relationship. It had to be very meaningful for Kyoko, as well, who was struggling alone without family support or a husband, raising a daughter, to find a kindred spirit in this sweet young boy. The whole thing is Tragedy.
Kazuma's flashback of the time how coldly he treated the previous Cat, his grandfather, which he clearly regrets afterwards. His grandfather never blamed Kazuma and all he said was "It's okay"
Ritsu's introduction starts out funny...then he reveals (while smiling) just why he apologizes so much. Because he feels like there's no good he can do in the world. Yeah even the comic relief character is a giant woobie.