This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Persona 4: The Animation
The small details the animation team added to the relationship between Yosuke and Saki really do help to make the latter's death all the more heartbreaking. For one, there's the fact that Yosuke had actually gone as far as to ask Saki out on a date, and there's the scene at the beginning of #2 where after being turned down by Yukiko, he perks up and says that Saki is the only woman for him. And then there's the crestfallen expression when Saki's death is announced and it's hard not to feel sorry for him in light of the context.
Yu's crestfallen look when it appears that the mystery has been solved and that there won't be a need for the Investigation Team to hang out anymore.
In the next episode, Yu suffers a Heroic B.S.O.D. and shows his nightmare: a world in which the investigation is over and one by one the team members distance themselves from him. It's a very sad and heartbreaking deconstruction of Fire-Forged Friends.
Yosuke's casual remark about how "it just goes to show that we were the only ones who thought we were friends," — followed immediately by Yu overhearing Kanji complaining about the group still meeting up for no reason and having to act friendly — hits particularly hard. In the end Yu is completely alone, unable to summon any of his Personas to defend himself because he has no connections to anyone any more.
Episode 14. Hisano. All our tears.
Episode 16. The anime rendition of Naoto's confrontation with her Shadow. Setting aside the possible issues about the character for a while, it's rather... well, heartbreaking to see the until then coolheaded Naoto have a breakdown when she's at the end of a brutal "The Reason You Suck" Speech about her identity as a whole.
The insert song / special ending theme, "True Feelings" is the arguably the most heart-wrenching part about the episode, and maybe the entire show. It's a song about Nanako yearning to visit her mom in heaven and telling her dad that she will always love him.
Episode 21. Just... damn. Nanako's kidnapping, and Yu's subsequent breakdown.
Episode 22. Nanako's EKG flatlines. To rub salt in the wound Dojima rushing desperately to reach Nanako's room in time, only to arrive too late.
The episode opens with the entire team crying over Nanako's death and Dojima trying to get to Namatame's room
Yu breaks down cryingin the snow after Nanako dies. He asks Yosuke if he did the right thing letting Namatame live, who doesn't say anything, just gives Yu a shoulder to cry on. And the poor dude does. The dub makes this scene even more depressing thanks to JYB's damn good acting.
While Namatame is a really crazy person, the scene in which he fails to save Mayumi from dying in the Midnight Channel is surprisingly effective in these regards.
Teddie vanishing into the fog, broken and depressed
Episode 25. Yu's departure. It's both sad to see him go, but also happy since it's not necessarily goodbye forever, and it's clear how much he valued his time in Inaba. The last shot of him still holding his glasses is particularly effective.
Episode 26. After everyone seemingly dies at the hands of Izanami, Yu goes into a Heroic B.S.O.D. / "Groundhog Day" Loop and almost goes insane. It takes a battle with Margaret and facing his own Shadow to snap him out of it all.
Even worse? As you likely know from the game, after a certain point, Izanami begins having the party swallowed into the shadows. Yu is forced to watch as they're all dragged under, one by one. Whether in Japanese or in English, his agony at the horrific scene before him is palpable.
Yu: Don't do this...please, stop!I DON'T WANT TO SEE THIS...!!!