This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The Big Bang Theory
Leonard's Despair Event Horizon in "The Nerdvanna Annihilation" over Penny's anger-induced jabs at the four's lifestyle.
Leonard's Hilariously Abusive Childhood is, like Amy's past, funny but sad. For instance, he never had a birthday party as a kid, and he essentially had to give up his childhood to become the genius he is now. Poor guy.
In "The Friendship Algorithm", Sheldon is at a bookstore looking for a book about making friends when he strikes up a conversation with a little girl. They get along, with Sheldon offering to take her to a zoo before Leonard drags him away because of how bad it looks. It's set up as a gag and it works as one, but it also fits here because we (the audience) know, for all his quirks and annoying habits, would never do something like that to her and she was probably relatively safe with him. Child abduction and abuse are horrible, it's just people have to assume the worst even from someone who wouldn't even have a sexual encounter with a willing woman his age (Amy, Season 5). The absolute worst part: Sheldon was trying to learn how to make friends and that girl probably would've been a close friend (It's Sheldon, would it have been weirder than half the stuff he does?)
Really, it was sad not because of the specific events but because it once again showcased that on an emotional level Sheldon isn't much older than that girl, which has been the source of most of the problems in his life.
Howard: When I was eleven my mother got me one to help me sleep after my dad left. I used to pretend my dad had moved to the planet Melmac and Alf was going to bring him back... but he never did. *Tearfully* Where's my daddy, puppet? Where is he?
Amy's isolation in "The Isolation Permutation" rings true, especially since her interactions with Penny made her ecstatic to be friends with a cheerleader type and to be excluded at all brings back ALL those painful memories.
Howard going to see Bernadette after she finds out that he previously hired prostitutes, had sex with his cousinnote second cousin! and had a threesome with Raj and a women dressed as Sailor Moon. The show comes this close to making you think they are about to break up.
Bernadette also has a small breakdown when she learned Penny knew all about his past and kept silent because she didn't expect them to go past "meeting his mom" or "sex." That must have been really difficult for her, feeling like the whole world was lying to you.
Everyone's What the Hell, Hero? to Penny after discovering that she has never told Leonard that she loves him. She admits that she does to Amy and Bernadette, but hasn't told Leonard simply because she thinks he'd make a big deal out of it.
Becomes sadder when you realize that Leonard grew up with an emotionally distant mother who never said it either. Is it any wonder why the poor guy simply wants to be told it every now and again?
Even worse - another interpretation of that scene is that she doesn't love him. She seems like she's only really saying it because otherwise she'd look like she was just using him for sex.
A jerk he sometimes might be, but you can't help feeling sorry for Raj in this situation. It seems funny to outsiders, but selective mutism is real and awful, awful condition to suffer from.
Howard's story to Bernadette about how he used to put on a magic show for his mother, and that it would help her forget how lonely she was.
There's just something so heartbreaking (even if it was part of a genuine heartwarming moment right before) in the scene where Leonard goes back to his apartment to let the news that Penny loves him sink in. It makes it seem like he genuinely didn't believe she did before. You really just want to hug the guy.
Was a little depressing to hear ALL of the guys admit that they didn't do much "father/son" stuff with their dads when they were younger...
More than that, his other reason for wanting his Pop Pop back was because he didn't want his Mee-maw to be sad anymore. We very rarely see Sheldon show that level of awareness and empathy towards someone else, making it clear how much he adores his grandmother.
"The Bakersfield Expedition" was a spirit-breaking ordeal for all four guys as Leonard's car was stolen, Sheldon was hit with a Slurpee thrown from a passing car, and they were subject to ridicule at the diner where they finally got to call for help. Even SHELDON was left depressed by the whole thing. The fact that the girls got hooked on comic books while they were gone was a small bright spot in an otherwise depressing episode.
Lucy running out on her and Raj's date in "The Monster Isolation" and Raj's resulting Heroic BSOD leading to him deciding to completely shut himself off from the rest of humanity. Later when she comes to apologize we find out that she has many of the same issues and anxieties that he does and ran away because she was scared.
Raj's complete and total heartbreak when Lucy breaks up with him via text message.
The letter from Howard's dad in "The Closet Reconfiguration", which does nothing but give Howard a Heroic BSOD upon remembering he still had it, and sealed. Even when the rest of the crew come up with a ploy to tell him a plausible message that the letter could've held (since he doesn't want to know what the letter said), he's still holding back tears as each person goes through their scenario.
YMMV, but anyone else feel for Raj during Howard's song to Bernadette when Howard calls her his best friend? I mean, Raj is coming off a breakup with Lucy, is watching Howard celebrate all the things Raj doesn't have, and on top of that, hears Howard admit that he's been replaced as his best friend. Kind of Fridge Sadness in a way.
Penny sees Lucy at the restaurant and bugs her to see Raj in person after she dumped him via text/e-mail. Raj is happy to see her again, but she tells him that she's seeing someone else. Now it seems like Raj has SEVERE trust issues... Penny sets him up with another girl and, without any provocation at all, IMMEDIATELY suspects she's already got a boyfriend and accuses her of lying about it when she says she doesn't. This guy needs a break SOON.
Although it was played for the gag, the scene where Amy imagines her life if she never met Sheldon, showing her sitting completely alone in her apartment, celebrating her own birthday with a tiny cupcake. Then her breaking into tears while halfway through singing herself happy birthday, is really quite heart breaking. It defiantly hammers in the fact that before she met him, she had no one what so ever who cared about her.
Stuart imagining that he's cool and dating Penny starts off quite funny, until the scene cuts back to reality showing him sitting alone in a near empty restaurant, the look on his face when he zooms back and realises how alone he is, is really quite sad.
"The Proton Transmogrification" is all about the death of Arthur Jeffries, A.K.A, Professor Proton. Sheldon at first appears to take the news quite well, but then he has a breakdown and locks himself in his room. He dreams that Arthur visits him, and there Sheldon explains that since his father and grandfather died when he was young, with Professor Proton dead, all the men he looked up to were now gone. Arthur gives Sheldon one last piece of advice: to appreciate his friends. When Sheldon wakes up and sees Leonard, the first thing he does is give him a heartfelt hug, an unusually emotional move from the typically detached Sheldon.
Also Professor Proton's first episode, when Sheldon admits that as a child, he didn't have any friends. He sounds SO vulnerable when he explains how Professor Proton would do science with Sheldon every afternoon.
Just when you think life couldn't treat Stuart any worse, his comic shop burnt down.
Stuart being the woobie is just not funny anymore. Tropers who are battling depression themselves just want to give that poor guy a hug and tell him that everything is gonna be alright.
Sheldon's mental breakdown that life is changing and it needs to stop. He takes a trip on a train to let him straighten his ideas.
Amy had an emotional breakdown at the end of the episode once it finally sunk in that Sheldon was gone.
In "The Space Probe Disintegration", Leonard and Sheldon talk about how they make compromises for each other, leading to Leonard telling Sheldon that the only reason he doesn't live with Penny is because of Sheldon (who had an emotional breakdown the last time the subject was brought up). Sheldon apologizes and tells Leonard he's all right with Leonard going to live with Penny, and starts crying because he's "imagining a world without my best friend in it". Leonard says he's only going to be living across the hall from him:
Sheldon: Either way, I just wanted to say I'm aware of how difficult I can be, so I just wanna say... thank you for putting up with me.
Leonard's voice cracking when he replies with "Buddy..." only makes things worse.
Howard's mother passing away and Sheldon's genuine consolation.
The final moment of that episode qualifies, too — while Howard and Bernadette travel to Florida (as Mrs. Wolowitz died there), the rest of the friend circle gathers in Sheldon and Leonard's apartment and reminisces about her, ending with Leonard leading a toast to "Mrs. Wolowitz, a loving mother... to all of us."
What makes it even worse is that due to Howard's feud with Stuart after the latter began living in the Wolowitz house and being spoiled by Debbie, it's heavily implied that he had stopped visiting frequently.
The whole thing gets ramped Up to Eleven when you remember that this is a case of Real Life Writes the Plot — the actress who provided the voice of Mrs. Wolowitz passed away for real, and so the entire plotline was added to the show. To at least some extent, the grieving shown by all the actors is genuine.
"The Intimacy Acceleration" has several, but the worst is Howard tearfully recalling that he was too busy to drive his mother to the airport to catch her flight to Florida; he made her take a taxi instead. He lost the opportunity to spend more time with her, and truly Never Got to Say Goodbye.
A subplot of the episode involves the airline losing the bag containing Mrs. Wolowitz's ashes. But the airport worker trying to help Howard and Bernadette isn't a Jerkass: she doesn't really know what to do with the situation (which is already incredibly stressful), and she's being forced to deal with two understandably upset but extremely angry people, one of whom threatens to kill her if the ashes aren't returned right away.
The title of the episode refers to Penny and Sheldon taking a test that can apparently make people fall in love within minutes. One part of the test is revealing secrets to each other. Penny confesses that deep down, she wishes that she was as smart as the rest of the group, hinting that she might be insecure about her own intelligence. Sheldon, meanwhile, notes he wishes he could "read minds"—that is, understand human interaction and emotion as well as Penny and others do. There is a kind of Fridge Sadness here; Sheldon is so emotionally stunted that he considers socializing with others and having basic empathy a superpower. It also reveals that he genuinely can't differentiate between people being annoyed at him or other things; again, Fridge Sadness suggests that he's so used to people finding him bothersome that he expects it to happen whenever he meets someone new.
In "The Leftover Thermalization", a blackout at Howard's mother's house means that all the food in the freezer is thawing, and there's no alternative but to cook it all. Howard gets emotional about having to cook the last meal his mother ever made, noting that she believed her cooking could cure anything. He invites all his friends over, saying that it's like her mother is feeding them one last time.
The moment when it seems to finally dawn on Howard that he really isn't ever going to see his mother again. The man can only get teared up in his wife's arms.
In "The Commitment Determination", Sheldon offends Amy for the umpteenth time. Sheldon doesn't understand what he did wrong, but Amy is really upset because he was thinking more about The Flash series more than her during their fifth anniversary of their first date. Eventually, after stumbling through the episode with his Dumbass Has a Point behavior when it comes to relationships, he Skypes Amy. Amy, sick of Sheldon's inability to read people and general selfishness, tells him she wants to step back in their relationship and ends the call. Sheldon, confused, turns to his Gollum figure and asks the ring expert what to do with the one he just bought. Unlike other serious moments in the show that may be spoiled by Mood Whiplash, there is no laughter after this turn of events. It just cuts to the credits.
Leonard and Penny are on their way to Las Vegas to get married, both are excited and then Leonard reveals that there was an incident overseas when he drunkenly made out with a drunk lady. Penny is shown to be disappointed by the news and more peeved about the timing he chose to drop such news on her. Also, she was always faithful to him.
The season premiere was somber to say the least. Leonard and Penny are finally married, but their relationship may never be the same with all the tension related to Leonard's Season 8 finale admission (AND the fact that she's a co-worker). On top of that, Sheldon and Amy seem to be officially broken up and Sheldon is having trouble dealing with it...
After Leonard moved in with Penny, Sheldon is worried that he is going to see less and less of Leonard and lists all the reasons why they would have dinner with each other on special occasions. The first two reasons are funny only for it to end with him claiming Amy will marry someone else, someone better than Sheldon. It seems the idea he may have permanently lost Amy has finally sunk in, and it's hit so hard he'll actually resort to self criticism. Sheldon has such a sad look on his face that he really sells it.
After Sheldon convinces himself to go to propose to Amy, he walks to her apartment and sees her returning from a date and receiving a kiss. He doesn't say a word, just puts the ring back in his pocket and walks away. It's a credit to Jim Parsons' acting ability that you can tell how utterly crushed Sheldon is without speaking.
The depth of Sheldon's feelings really hits Leonard and Penny hard after they find out about his plan to propose. When Sheldon snaps at Penny "I SAID I'M FINE", it looks like she's trying not to cry.
In The Mystery Date Observation, Amy finds out she is dating a Sheldon Cooper fanboy. While the laugh track is quite amused, the fact that all the things he keeps raving about were things that involved Sheldon being a selfish Man Child towards her gets kind of depressing.
In The Platonic Permutation so they don't waste the tickets, Sheldon and Amy decide to go to the Aquarium café Thanksgiving Dinner as friends. Though the food proves to be awful, the two have a fun time together. So much so, that Amy begins to remember why she wanted to date Sheldon in the first place and begins to miss their interactions. That night, she calls him and asks if they can get back together. Sheldon, still having problems with their break up and getting over her, turns her down stating they need to stay friends for the moment. Amy quietly accepts this, while looking heartbroken. Worse still, it's the end of the episode, so we're just left with a look at Amy's disappointed face.