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Tear Jerker: Elementary
Sherlock explaining to Joan why he can't accept his one-year sobriety chip: it's not his one year anniversary of sobriety, because the day after he entered rehab, he snuck out to get drugs to deal with his crippling withdrawal. He's shuddering and his voice seems close to breaking. He looks almost like he's going to start crying.
Sherlock: It just- it sounds like a mere detail, but I am a man of details and, it- it matters to me.
In "Step Nine", You feel for Mycroft as he tells Joan that he couldn't even bring himself to contact his own brother to tell him he had cancer and needed a bone marrow donation. His cancer treatments made him rethink his life and his relationship with Sherlock.
The scene in "Solve For X" where Joan describes the death of a patient, how it drove her out of the medical field, and how she's haunted by guilt over the incident.
In "Poison Pen" Sherlock Holmes reveals more about his backstory—merciless bullying and isolation at boarding school.
Abigail Spencer is this personified.
In 'We Are Legion', we have a son who kills his father for sexually molesting him and possibly going on to molest his younger son and tries to frame the family's nanny for the crime. Said nanny was accused of poisoning her abusive father when she was fifteen and lost her entire life and all her friends due to the controversy. As soon as she heard of what happened to the son, she immediately took the fall for it because she loved him and couldn't bear to see his life ruined like hers had been and in a way, she says she is finally paying for her crime.
A recurring moment in Season 2 is the effect of Moriarty's betrayal on Sherlock. It's quite tragic to see such a brilliant man continue to struggle with his contradicting feelings.
Sherlock's speech to his NA meeting at the start of “The Marchioness.” Sherlock talks about how his powers of observation can overwhelm him, especially in today's Hi-Tech society. In a moment of meta commentary, Sherlock wonders if he was Born in the Wrong Century. It also nudges the edge of Deconstruction, basically implying that someone like Sherlock Holmes, with amazing powers of observation and deduction that he can't simply "turn off," couldn't be a functional human being in modern society.
It gets even sadder when you realize that his belief that if he'd lived in the Victorian Era he wouldn't have been an addict is wrong.
The end of "Tremors". When Holmes' antics finally go too far, a suspect takes a shot at him. Bell takes the bullet instead, sustaining a nerve injury that might impair his ability to be a detective. Even worse, their relationship is now more strained than ever.
"Internal Audit"'s Victim of the Week is just plain sad. Not only does he turn out to be guilt ridden for creating a Ponzi scheme and would have been Driven to Suicide had he not been murdered first, it turns out the charity he devoted a part of his life to was really just a front for money launderers and he was killed for attempting to reveal that fact. Sherlock puts it best when he states that it's rare for someone to be totally good or evil-he may have been a greedy Corrupt Corporate Executive, but he was a person too, and he was punished for his virtues.
"The Diabolical Kind" has one from Moriarty, of all people, in the scene where Sherlock is yelling at her about the code she put in the sketches and she's on the verge of tears, and the scene where the kidnapper's on the phone and puts Kayden on and Moriarty flinches. Especially upsetting after The Reveal that Kayden is Moriarty's daughter.
Joan's explanation of why she volunteers with the homeless. Her biological father is schizophrenic and lives on the streets of New York City. There's no tears or drama, just a calm, sad acceptance of the situation and a compassionate determination to help other homeless people.
Lestrade's breakdown in "Ears To You", wherein he finally admits to everyone (not the least himself) that he's nowhere near as clever a detective as everyone thinks he is, and further that he's relied on Holmes for so long that whatever skills he might have had on his own as a detective have been lost to him and he doesn't think he can do it any more. He ends by bitterly implying that the same thing will happen to Joan eventually: that Sherlock will get bored with her and move on to a more interesting project, and leave her completely incapable of functioning...and he advises her to "enjoy the ride while it lasts."
The Bittersweet Ending of Bell's storyline in "The Hound of the Cancer Cells". A respected teacher whom Bell has befriended is battling a local drug lord who's on trial for murder. When the only witness (a pregnant student the teacher was protecting) gets cold feet, the teacher sees only one way to make sure the drug dealer doesn't walk: a Suicide Attack that winds up killing both men, which the teacher realized would happen all along.