This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Star Trek: Deep Space Nine
"You always said I looked good in a tuxedo."
"The Visitor" is possibly the saddest thing on television that doesn't involve Fry's dog.
Jake: Read the inscription.
Sisko: "To my father, who's coming home."
It actually isn't that bad the first time through. The second time, however, all bets are off.
For context, the episode features an alternate future where Jake, now an old man and reclusive former writer, tell a young student his life story, which diverged after Captain Sisko was seemingly killed in an engineering accident. He moves on to some degree, but every several years his father reappears in reality for a few minutes each time. When Jake realizes what is happening and why, he quits his successful writing career and lets his marriage collapse in order to go back to school and become the foremost expert on the physics causing his dad's condition. Even when, after an attempt to save him fails and Sisko begs his son to move on with his life, Jake is unable to do so. Finally, as an old man, he waits for his father to reappear so he can kill himself and break the cycle. The hardest part to see is Ben Sisko trying to help, seeing his son who is older than he is, willing to give up everything just to be with his dad again.
Or even before the ending, Marritza's heartbreaking confession when he can't maintain the masquerade* He was pretending to be infamous Cardassian butcher Gul Darheel, intending to be caught and executed for Darheel's crimes to force Cardassia to face up to what it had done to Bajor any longer. Even Kira begins to tear up.
Kira: You're Marritza, aren't you?
Marritza: You mistake me for that bug? That whimpering nothing? Oh, you stupid Bajoran girl. Don't you know who I am? I'm your nemesis. I'm your nightmare. I'm the Butcher of Gallitep.
Kira: The Butcher of Gallitep died six years ago. You're Aamin Marritza, his filing clerk.
Marritza: That's not true. I am alive. I will always be alive! It's Marriza who is dead. Marritza, who was good for nothing but cowering under his bunk and weeping like a woman. Who, every night, covered his ears because he couldn't bear to hear the screaming... for mercy... of the Bajorans... [collapses into helpless sobbing] ...I covered my ears every night, but... I couldn't bear to hear those horrible screams. You have no idea what it's like to be a coward. To see these horrors, and do nothing. Marritza's dead. He deserves to be dead.
Sisko: So... I lied. I cheated. I bribed men to cover the crimes of other men. I am an accessory to murder. But the most damning thing of all... I think I can live with it. And if I had to do it all over again, I would. Garak was right about one thing, a guilty conscience is a small price to pay for the safety of the Alpha Quadrant. So I will learn to live with it. Because I can live with it. I can live with it...
Suffice it to say that if Deep Space Nine wants you to cry, you will cry.
An unusual entry, I know, but, Nog's true reasons for wanting to join Starfleet always made me feel absolutely awful. The look on Captain Sisko's face throughout made it even worse; he almost looked ashamed of himself.
Oh he's utterlyashamed of himself- from the start he'd never considered Nog's request to join Starfleet as anything other than some devious Ferengi scheme for profit and in this scene he virtually bullies Nog into explaining himself, even physically grabbing and shaking him. Then he finds out that Nog's reasons are heartbreakingly personal and tragic and he realizes he's forced the young man to admit that his own father (whom Nog still loves dearly) is a failure because of his own cultural and racial prejudices. Fortunately, he does make it up to Nog.
It's also Hilarious in Hindsight, considering that Nog's failure of a father becomes the Grand Nagus and leads a successful top-down revolution of the way Ferengi do business.
... But only because Rom began doing the same thing that Nog was doing- not blindly following cultural rules. Both became extremely successful, holding titles of great import- First Ferengi in Starfleet and Grand Nagus- but only by realizing that continuing what they were doing, simply following what they thought society expected, was not sufficient. If that's not a cause for Manly Tears, I don't know what is.
Time's Orphan, 8-year old girl stranded, alone, 300 years in the past. Brought back as a feral girl 10 years (relative to her) later. Eventually, her parents have to send her BACK as her only shot at being happy. Sorry chief, looks like being The Woobie runs in the family.
This one ends up inverted though. Feral-Molly ends up arriving in the past mere minutes after her younger self and ends up performing a Heroic Sacrifice to send the little girl home, choosing to negate her own existence in the process. So it's a happy ending, but still tear jerking on behalf of Feral Molly.
That only added to the tears. Would list all the things that add to the tears but that turned into a synopsis (minus the Kirayoshi subplot). This troper would put this episode on a Tear Jerker level with Jurassic Bark (if not higher). After watching it had to go back to the Ferengi episode just prior to stop sniffling.
Even the Kirayoshi subplot becomes a Tear Jerker in hindsight once you realize that it inspired Jadzia and Worf to have a baby of their own, only for Jadzia to be killed by a possessed Dukat as she's praying to the Prophets for help with her fertility.
Hell, the first episode starts with a Tear Jerker as Sisko is dragged kicking and screaming from his wife's half-buried body out of his quarters. His broken voice is haunting, especially at the end where he seems to suddenly realize he is going to never be with her again, with nothing left to mourn.
Sisko: "We can't leave her here."
Lieutenant: "We've got to go now, sir!"
Sisko: "Dammit, we just can't leave her here! Oh no!"
Even before that, we get to see The Battle of Wolf 359, the battle that left 39 starships destroyed and 11,000 men and women killed or assimilated. On TNG, we got to see the aftermath. Here, we get to witness not only the ships being mercilessly blown to bits in a vain attempt at destroying the cube, but some of those 11,000 as they died, all the while the audience knowing that it was all in vain thanks to Locutus out-thinking the entire fleet thanks to Picard's knowledge and experience.
And later when Sisko meets the Prophets and has to confront his own refusal to move on because he doesn't know how to live without her:
Before that, when the realization hits him, the simple, devastating line: "I never left here."
And then, two years later, during "The Search," he has to drag Dr. Bashir away from (the fake) Garak's body, an act which in the novelization he explicitly compares to having to be dragged away from Jennifer. Yikes.
Weyoun... poor, poor Weyoun. Not just his death(s), but his entire existence, really. Particularly the "defective" one who died in Odo's arms after a Heroic Sacrifice. But even the look on one of the regular Weyouns's face when one of his Gods (who would throw away his life in a heartbeat, if she had a heart at all) refers to him as a trustworthy and loyal servant.
The look on his face when the female Founder calls him the only solid she ever trusted. He looks so pleased to hear that, you get the feeling that he lived his entire life, the lives of every Weyoun that came before him, to hear these words. And he probably has, as well.
Sisko: Do you really want to give up your life for 'the order of things'?
Remata Klan: It is not my life to give up, Captain-and it never was.
There's also "Ties of Blood and Water" and the death of Tekeny Ghemor. Becomes bittersweet when Kira, after initially refusing to speak to him after discovering that he took part in an attack during the Cardassian Occupation (he was nineteen years old and was told that the people he killed were smuggling weapons), chooses to forgive the man who has come to think of her as a daughter and buries him on Bajor beside her real father (whose dying moments she had been unable to face, choosing instead to go out and hunt down the Cardassians who had killed him). She found the strength to stay by Tekeny's side and her description of his final, struggling breaths is heart-wrenching.
The episode "Life Support" forces Major Kira to deal with slowly losing the man she loves as he sacrifices himself to complete an important and symbolic peace treaty. He keeps insisting on riskier and experimental medical treatments in order to continue his work, supported by both Kira and the Kai. When the treaty is signed and all the costs and consequences catch up to him, Kira is left with only a last chance to say goodbye and tell him how much she loved him, but it's already too late for him to be able to hear or understand her.
Also, the way that he was reduced to little more than a tool for Winn, so that she could claim credit for finishing the negotiations after he was incapacitated. After the negotiations finish, Winn is almost too enthusiastic about pulling the plug and letting him die, now that she has taken credit for his most important and lasting achievement.
"Heart of Stone" is the first episode in which Odo reveals that he has been secretly in love with Kira for years. He confesses this to her when it seems like she's trapped in a deadly situation and she's trying to persuade him to leave her behind. She tells him, "I love you too" and that she felt the same way for some time. This is the crucial mistake that tips Odo off that's an impostor Kira, he knows the real Kira sees him only as a friend and wouldn't be the type of person to lie about it in order to comfort him. Later, when Kira asks how he figured out it wasn't her, he explains that the impostor "said something she would never say."
The thing about this episode that made this troper cry was how Kira was slowly being crushed by the crystal around her, her voice getting more and more choked and panicky, and her heartbreaking attempts to make light of the situation and then, when resigned to death, get Odo to leave her. Odo is completely powerless to help the woman he loves and he looks like his whole world is ending. It's really distressing to watch, even if you know "Kira" is an imposter.
Also, there's the off-handed way he says to Kira that the impostor said something she wouldn't - he has already accepted that Kira would never love him and is able to say that so casually like it was a statement of having enjoyed some food that Kira is deathly allergic to or something, rather than 'I'm in love with you too.'
Oh god, "Crossfire." All of it. Even if you ship Kira/Shakaar, it's still sad.
Jadzia's death in "Tears of the Prophets" was easily one of the saddest sequences in Trek's history. And poor Worf. Even he can't keep a stiff upper-lip about this. His roar at the end is concentrated tear-jerker-ness. (Sure, it's Klingon ritual to warn the dead another warrior is coming, but be honest: Worf just screamed because the woman he loved is dead in his arms, he wasn't there to help her, and he couldn't do a damn thing to save her), and then his sobbing prayer over her body.
The actual ritual involved holding open the dead's eyes and roaring but Worf forgoes that part because he can't even bear to look at her.
Worse, this is the second time this has happened to Worf.
And in the next two episodes, his ongoing grief (smashing up Vic's place after demanding he sing Jadzia's favorite song, and Vic indicating that it was far from the first time) over her death, culminating in tears of joy as he accomplishes his goal of honoring her death in a great battle and assuring her entrance to Sto-Vo-Kor.
Sisko breaking down over her coffin, telling Jadzia that he doesn't know what to do and that he still needs her help. He's so shaken that when he goes on leave, he takes his prized baseball with him, which Kira recognizes as a sign that he's not sure he'll ever come back.
A little thing that's heartbreaking all on its own - the Defiant returns to DS9 after the victory at Chin'toka, and Worf RACES to the infirmary. Seeing him running, almost panicked is a jarring moment all on its own, and really hits home that this is happening, that Jadzia is dying.
Also, "The Quickening". Bashir is trying to find a cure to a seemingly incurable disease which is present in a dormant state in all the people on the planet until the day it "quickens" and leads to their death. Shortly after distributing an antigen he thinks will cure the disease, his volunteers' conditions abruptly worsen and Bashir realizes that the EM fields from his instruments have severely hastened the progress of the disease. All around him are screaming patients in horrendous pain who beg for euthanasia to end their suffering. They all die except Bashir's first volunteer, who is heavily pregnant, but she has quickened which means her death is soon to come. Bashir stays with her and tries to keep her alive long enough to give birth. She lives just long enough to learn that her baby does not have the disease because the antigen crossed through the placenta and gave the baby immunity.
Consider that Bashir, at the start, is confident—even cocky—that modern Federation medicine and his own brilliance will be able to overcome this disease. Consider also that he seems to have forgotten he's overlooked that he's trying to beat a Founder-devised and -engineered disease, and the Founders seemed to have mastered genetic engineering beyond anyone else in the entire galaxy back when Earth was still having mere Eugenics Wars. In the end, he does win, which in context is actually something of a moment of awesome for him, but oh, the price they pay for it. Now flash forward to the female Founder's intended last stand in season 7. Isn't that just like the Founders?
To be entirely fair to Bashir, it's not entirely unreasonable for Bashir to assume that Federation Medical Science could cure these people, as similar "miracle cures" for sick populations had been whipped up by the medical crews of the various Enterprise ships.
This episode hits me particularly hard as a scientist. It conveys so well how dearly researchers want to help people, and how heartbreaking setbacks can be because we know that we can't rush science, but there are real people suffering and dying while they wait on cures.
"Children of Time". The last ten minutes.
The death of Enabran Tain, who was not only Garak's mentor but also Garak's father as well, in "In Purgatory's Shadow".
"The Begotten". Any aversion of Infant Immortality is going to be a Tear Jerker, but this one is made worse by how happy the baby Changeling made Odo.
"Please, don't die. I was going to teach you how to turn into a Tarkalean hawk. Remember?"
The number of Moments Of Heartwarming in this episode for Odo, Dr. Mora and Kira, only make the ending that much more bittersweet and painful. The fact that the baby Changeling was reaching out to Odo in such a way and the connection he had with it only makes it more so.
Kira and Odo's parting scene as Odo enters the Great Link in "What You Leave Behind."
"Hard Time", O'Brien is implanted with the memories of a 20-year prison sentence, during which he was kept sane only with the help of a fellow prisoner, Ee'char. After he's "released" and returns to Star Trek: Deep Space Nine, the prisoner appears as a hallucination to help him get over the experience and regain his humanity. The scene where Bashir attempts to talk O'Brien out of suicide, and the true story of Ee'char is revealed, is heart-wrenching.
Ee'char: Be well, Miles.
The end of Rejoined - Jadzia Dax is willing to throw away immortality and endure permanent exile from her home civilization to be with her once and hopefully future love. The ending, after the passionate argument asking her former wife not to leave... they lock gazes across the Promenade... and Dax's lover leaves forever, unwilling to make the sacrifice. Dax has simply the most heartbreaking expression...
The battle in "The Siege of AR-558." The haunting, mournful music playing over the phaser fire and screams of battle makes it even harder to watch dry-eyed as the away team and the Starfleet officers who have been slowly dying, both physically and psychologically, fight a brutal and ugly battle for the sake of a hunk of technology and many of the episode's characters are killed.
The worst part of this comes later on when the Dominion and Breen manage to retake the Chin'toka system in "The Changing Face of Evil". All the Starfleet personnel who died during the siege died for nothing because in the end, AR-558 and the comm hub end up back in enemy hands. Talk about Shooting the Shaggy Dog.
"Doctor Bashir, I Presume". It's revealed that Bashir was mentally impaired as a child, which led to his parents genetically altering him to be much smarter. He's spent his entire medical career holding back, in the fear that if he was just a little too smart he'd be caught, kicked out of medicine, and made a pariah for something he has absolutely no control over. His confrontation with his parents, however, is the worst.
Bashir: You used to be my father. Now, you're my architect. A man who designed a better son to replace the defective one he was given.
Thankfully there's a happy tearjerker when mother and father fess up about what they did to the authorities and apologize to Julian, ensuring that they will bear the punishment for their actions and saving both his Starfleet and medical careers.
The death's of two of Trek's greatest and most well known (as well as popular) Klingons, Kang and Koloth. In the end, Jadzia sums it up best.
"It's never a good day to lose a friend."
Kor's singing somehow makes it even more heartwrenching.
The death of one of the greatest Klingon warriors the galaxy has ever known, you died well Kor.
Blood Oath and Once More Unto The Breach become this way with the passing off all three of the Klingon trio.
Odo rejoining The Great Link, saying goodbye to Kira in the tuxedo.
The ending of Necessary Evil , when Odo realizes that Kira not only committed a murder he thought her innocent of, but kept the truth from him for years. Kira, near tears, confesses she wanted to tell him, but didn't want to lower his opinion of her - what he thinks of her is very important. The last line of the episode is gut-wrenching:
Kira: (brokenly) Will you ever be able to trust me the same way again?
Odo: (Looks up at her in a way that breaks your heart in pieces. He can't answer.)
In "For the Cause," Sisko has learned that Kasidy is smuggling for the Maquis. Right before she ships out on a rendezvous he intends to follow her in the Defiant to and catch her and the Maquis in the act, he goes down to speak to her, practically pleading with her to join him and drop everything and take a runabout to Risa, just so that she'll be out of the line of fire. He is desperately trying to get her to let him help her out of this, to not be implicated, but he can't say it directly without tipping her off. It's so devastating watching him trying to offer her this chance without actually saying so, and then the look on his face when he realizes that he can't talk her out of it...
In "Family Business" Quark and Rom have their only truly serious fight when their mother Ishka is accused of making profit (illegal for Ferengi females). After Quark and Ishka argue (where Ishka scathingly points out that Quark and Rom's father Keldar was a business failure) Rom confronts Quark and tells him their mother is right and their father was a failure, provoking Quark to attack him. The two brothers brawl around the room, knocking things over until their mother separates them, reassuring Rom she'll be fine and telling Quark to do what he wants before breaking down in tears once her boys have left the room. It's jarringly upsetting seeing Quark and especially Rom being so violent with each other, made even worse when you see how badly they upset their mother.
In Captive Pursuit, the Tosk is a sentient creature from the Gamma Quadrant which has been genetically engineered to be the perfect prey for an entertaining hunt, and indoctrinated to desire no other life. Offered asylum by the Federation, it refuses even in the face of being returned as a living captive, in dishonor, subverting the My Species Doth Protest Too Much Star Trek fans would've expected in such a plot. Its speech is a Crowning Moment of Tear Jerker:
At least Tosk gets its way, as far as that goes: released back into the Gamma Quadrant, to be hunted to an honorable death (that's the most respectful good-bye it knows to share with its only friend, O'Brien: "Die with honor".)
Don't forget the sequence of memories from "What You Leave Behind" as our heroes reminisce about the past seven years before going their separate ways. Try watching that without tearing up.
At the end of "Hippocratic Oath" O'Brien and Bashir offer to take the Jem'Hadar commander with them. He elects to stay behind as he's responsible for getting his men into this situation and can't abandon them.
At the very end of "Sacrifice of Angels", when Garak learns of Ziyal's death. It seems subdued, especially compared to Dukat's anguish, but it's also lacking in his usual theatrics; for once, you get the impression that the practiced liar isn't putting on a show.
Kira: She loved you. Garak: I could never figure out why. I guess I never will.
Kira breaking down and sobbing at the death of Kai Opaka. Until this point, Kira has been angry and determined, but this? This BREAKS her. As Kai, Opaka is the center of the Bajoran faith, it's through her strength that many Bajorans felt they could get through the Occupation. And she dies here, in an accidental crash on a forgotten moon, seventy thousand light years from Bajor.
Later, after Opaka has been resurrected by alien microbes, she breaks down again in the Kai's arms, as she admits how she has known only violence, and doesn't know how to let go of it, or how to forgive herself.
The villain of "Field of Fire" is a demonstration of what happens to Vulcans when they become a Shell-Shocked Veteran: they snap. Chu'lak was an officer on a Starfleet ship that suffered immense casualties, as in him being one of a handful of survivors. Being a Vulcan, Chu'lak attempted to suppress his feelings and was unable to do so leading to him go on a murderous rampage. Seeing a member of one of Star Trek's most revered alien races fall so low is rather heartbreaking.
Ezri: Tell me, why did you do it?
Chu'lak: Because logic demanded it.
The episode "Whispers" ends with A replicant of Miles O'Brien dying. It's bad enough for the viewer, who knows that the one who died never knew they were a fake—they thought they were the real Miles O'Brien—but one wonders how the Starfleet officers felt after they listened to the log entries that person left on the runabout....
The scene in "Accession" when Kira reveals that following her d'jarra would mean resigning her post. Both she and Sisko are on the verge of tears, a far cry from the depressed Starfleet officer who wanted nothing to do with Bajor and the hotheaded Bajoran who wanted nothing to do with Starfleet.