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Tear Jerker: The Ring
Most obvious are the tragic backstories of Sadako Yamamura in all continuties, as well that of Samara Morgan and Park Eun-Suh. All of them end up thrown down a well where they die and turn into Stringy Haired Ghost Girls.
Sadako being abandoned by her mother who commits suicide rather than deal with her depression and humiliation from the media after a botched demonstration of her Psychic Powers.
Sadako is raped by Jotaro Nagao, who discovers she is a Hermaphrodite and tosses down the well.
Tomoko's death in the first chapter of Ring.
Ryuji Takayama's death. He realises there are people outside his world(the virtual world known as the Loop) watching the events happening to him, and then telephones them begging for them to take him to where they are(the real world), before dying of a heart attack.
Spiral sees Kazuyuki's family die in a car crash but it is implied his daughter Yoko died from the Ring Virus beforehand. Kazuyuki then dies in hospital several weeks later.
Mai's Family-Unfriendly Death in Spiral when she gives birth to the reincarnated Sadako and her body is found crammed into a ventilation shaft on top of her apartment building.
Ryoji's suicide in Loop. After seeing Kaoru sleeping with his mother Reiko, Ryoji felt betrayed by both and ended his young life by leaping out of a window in front of both.
Kaoru's emotional final phone call with his father, and his attempted call to Reiko.
In Birthday, Toyama, Sadako's lover, reunites with Sadako before he dies.
The death of Reiko in Ring 2.
Finding Samara's corpse in The Ring. The discovery of Sadako's corpse in the original also counts (even though the sight of her skeleton - with her rotting skin slowly falling away from her skull - is very unsettling).
Ring 0: Birthday. Sob. Even though the viewer knows what's coming, it is still completely and utterly heartbreaking.
Another example from Ring 0, just before the already heartbreaking final scene - after attacking Sadako and throwing her down the well, Dr. Ikuma breaks down sobbing, begging Sadako to forgive him.
The ending of Ring 0 is just cruel. Sadako wakes up in Toyama's house, with her smiling lover standing over her, telling her it was all a dream. She goes to reach for him, only to touch the cold wet wall of the well. Realising where she is, Sadako screams for Toyama, and then looks up. The shot changes to looking over Sadako, who can only look up in scream in terror as she is sealed in darkness.
Masami's unfortunate death during Dr. Kawajiri's experiment to remove the psychic energy in her head.
The ending of Ring 2 is a Bittersweet Ending. Yoichi and Mai escape Sadako's curse, but both of Yoichi's parents are both dead. And poor Sadako is still stuck in the well.
Akane's backstory in Sadako 3D.
The pretty heartwrenching scene in Sadako 3D 2 where Fuko considers throwing her niece Nagi over a bridge, believing she is responsible for numerous murders and is Sadako's child. Nagi wakes up and starts crying, asking if Fuko hates her. They end up hugging, and Nagi reveals she can see how people will die, and hates being afraid, isolated, and unable to see her mother.
Akane's death in Sadako 3D 2 at the hands of a deranged policeman whose wife was killed by Sadako's curse.
Samara's fate at the end of The Ring Two where Rachel drugs her and seals her back in the well - and just as she was finally got what she always wanted; a mother who could care for her.