This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / American Horror Story: Murder House
As has been fondly remarked on the AVClub, Ben's A Date with Rosie Palms scene gives us a literal example of a TearJerker.
The look on Moira's face when she realizes her remains will never be found. The song that plays in the background makes it worse.
In episode, when Moira decides to Mercy Kill her mother, whose ghost then asks her daughter to travel together to the afterlife. Unfortunately, Moira can't. She seems to have a lot of these, doesn't she?
Chad regaining consciousness and weakly trying to reach out for Patrick before Tate shoots both of them. Shows that Chad still cared for Patrick even if Patrick had lost interest or given up on him. Made sadder when later Chad overhears Patrick telling Tate that he hates being stuck with him.
In episode 10, when a crying Tate reveals to Violet that she didn't survive her latest suicide attempt and that she was Dead All Along.
"You died crying. I held you, you were safe. You died loved..."
Not just Tate though, Violet finally showed a desperate and undeniable will to live... and then she finds out she died weeks ago. Her reaction to finding her own dead body was heartbreaking.
The fact that Violet's feelings of being neglected by her parents were entirely justified: Ben and Vivien have been so caught up in their own drama that they haven't even realised that she's dead. Sure, she's been present as a ghost and they'd probably be excused for not immediately realising she was actually dead, but she hasn't stepped out of the front door in weeks, and her school must have been contacting them to say that she hasn't attended in all that time - parents who gave even half a damn about their kid would surely have noticed something was amiss by this point. And there's the small matter of her corpse decomposing under the floor.
Vivien dying during childbirth, with Ben apologizing and telling her to live while Violet tells Viv it's okay to die, and that they'll be together forever. And all of this happened in episode 11, the penultimate episode.
Maybe it's just me but I can't help but feel bad for Lawrence almost every time he's on screen. he fell in love with Constance who was using him to get her house back, he just wanted someone to support his dream of being an actor and nobody really cared, his wife burned herself and his two daughters to death, Tate doused him in gas and set him on fire burning 70% of his body, he's called on to do the grunt work even though his burns cause him to limp and have an arm he can't properly use and whenever we see him in his dingy apartment it just feels so lonely and empty and sad.
Tate's confrontation with the students he killed.
"I'm supposed to be 34. I'm supposed to be married, and... and have babies...
Constance putting make-up on Addy in the morgue.
Even if one hates half of the ghosts in the house (Chad and Patrick, Hayden, the asshole brat twins), one has to remember: They are stuck in that housefor the rest of their existence. The Harmons, Moria, and arguably Lawrence's family and maybe Elizabeth Short are going to live in peace because they've found happiness with each other. The others? Nothing, because they can't find peace. It that's not saddening enough...