The stinger for the Bakeneko arc. After the credits are done and the Medicine Seller goes on his way, just when you think you're done crying, you see Tamaki and her kitten walking out of the house, finally together and free, laughing and mewing happily. And then you cry all over again.
From the same arc, the true reason why the Bakeneko is so murderous and hateful. It befriended Tamaki, who was being mistreated and forcibly used as a concubine by the family's patriarch, when the Bakeneko was just a young kitten. Over the years, Tamaki fed the Bakeneko at her own expense, giving it her food while saving none for herself. The patriarch's elder Jerkass son sneaked into the basement where Tamaki was held prisoner and tried to rape her in secret, but when he was caught, his father thought Tamaki had seduced his son and beat her to death as punishment. The Bakeneko tried to protect Tamaki, but she forced it to escape while the basement door was still open so it won't die senselessly for her sake. The Bakeneko's feelings of guilt and regret for failing to protect Tamaki twisted its physical form and turned the Bakeneko into the monstrous spirit it is today. For some, the entire reveal makes the Bakeneko become less Nightmare Fuel and more Woobie, Destroyer of Worlds.
The sorrowful and disgusted reactions of Kayo and Odajima throughout the whole thing truly hammers in how truly heartbreaking it is. To be working for someone who turned out to have done truly atrocious things can leave you with a very bitter taste in your mouth as well as feeling guilty that you were unaware the whole time and didn't try to stop it even though you were completely innocent.
The Bakeneko's Freudian Excuse is so tragic and horrifying that reliving the memory made it shed tears. Even the Medicine Seller felt sorry for it to the point of apologizing before he turns into his alter ego and exorcises it.
May also count as Heartwarming, but Kayo and Odajima setting up a burial shrine for the Bakeneko next to the family well where Tamaki's body was discarded so they can reunite in heaven also is this.
The aristocratic family's matriarch grieving the death of her daughter, who was the only child and the family's last hope of getting out of poverty. Even though she had a part in Tamaki's abuse and death, her grieving wails in both Japanese and English dubs can tug at your heartstrings.