"Encounter At Farpoint" features one of the most Tear Jerking moments in Star Trek history: Data's 'special assignment' to escort a 'rather remarkable man' on a tour of the Enterprise-D. What makes it so duct-damaging? That man was DeForest Kelley as Dr. McCoy from the original series, who would only appear two more times before his death (in the fifth and sixth movies, which premiered after TNG).
Eline: Now we live in you. Tell them of us... my darling.
Both the episode "Sarek" and Mark Lenard's last scene as Sarek in "Unification I" are beautifully sad in their portrayal of the tragic degeneration that comes with age to even the greatest men.
Sarek's battle with Bendii Syndrome is essentially the Vulcan equivalent of Alzheimer's. But instead of his memory, he is losing his emotional control, the cornerstone of Vulcan society and civilization.
Captain Picard struggling with Sarek's emotions after their mind meld in "Sarek" allows us to see Sarek's despair over the death of Amanda, his first wife, made even worse since Sarek feels that he never truly revealed the depth of his love for her. Patrick Stewart is at his finest as he gets the chance to show off his vaunted acting skills.
Picard: No! It is... it is wrong! It is wrong! A lifetime of discipline washed away. And in its place... [*laughter to anger to sadness at warp speed*] ...bedlam. Bedlam! [*frustration*] I am so old. There is nothing left... but dry bones... [*sobs*] ...and dead friends. Oh... tired. Oh, so tired. [*burst of anger*] No! This weakness disgusts me! I hate it! Where is my logic? I am betrayed by... [*wistfulness*] ...desires. I want to feel. I want to feel... everything. But I am a Vulcan. I must feel nothing. [*epic sobs*] Give me back my control. [*snaps to regret*] Per... Perrin. Amanda. I wanted... to give you so much more. I wanted to show you such... [*gasping, can't get the words out*] ...tenderness. But that is not our way. Spock... Amanda... Did you know...? Perrin, can you know... how... much... I... love... you? I do... love... you!
Sarek's plea to Picard in "Unification I" after Picard has come to find out why Spock is on Romulus.
Picard: Sarek, we're a part of each other. I know that [Spock] has caused you pain. But I also know that you love him.
Sarek: Tell him, Picard.
At the end of the episode, Spock expresses his regret that he and Sarek never mind-melded. Picard offers to meld with him, so Spock can experience what Sarek shared with Picard. Spock initiates the mind-meld... and his normally stoic expression cracks as he looks near to bursting into tears.
And then there's the Reality Subtext about it - Sarek's decline and eventual death mirror the timing of Gene Roddenberry's own. "Unification I" is also dedicated to Gene Roddenberry.
Kevin Uxbridge's confession at the end of "The Survivors" - he was a Douwd posing as a human who had fallen in love with a human woman, Rishon, and lived on a distant Federation colony world. One day the Husnock, a savage warrior race, attacked the colony. Kevin was a pacifist and refused to fight, while Rishon joined the other 11,000 colonists in defending their world. The Husnock wiped out the colonists and Kevin, in a moment of grief and rage at Rishon's death, obliterated all fifty billion Husnock in the universe with a single thought. Horrified, he sentenced himself to exile on the planet with only an illusion of his wife for company.
Picard:Captain's Log, Stardate 43153.7. We are departing the Rana system for Starbase 133. We leave behind a being of extraordinary power and conscience. I'm not certain if he should be praised or condemned, only that he should be left alone.
O'Brien talking his former captain out of his crusade in "The Wounded".
Maxwell: I'm not going to win this one, am I, Chief?
O'Brien: No, sir.
During that scene, the two of them singing the oh-so-appropriate "The Minstrel Boy".
Before that, O'Brien's reveal that his animosity towards Cardassians is because they made him have to kill during the war.
O'Brien: I don't hate you, Cardassian. I hate what I became, because of you.
The last fifteen minutes of "Dark Page".
To specify, Lwaxanna reliving the death of her first child, Kestra, while Deanna was still an infant.
Deanna:(last line) Tell me about her. I want to know everything.
Even before that there's Deanna meeting the memory of her father, who all but begs her for them to be able to talk this one last time, and Deanna's tearful response. There's a reason they call the trope Good Troi Episode.
Deanna: Goodbye, daddy.
Before "Dark Page," there was "Half A Life," which had Lwaxana fall in love with a man from a species who kill themselves at sixty, to spare them and their families from the ravages of age, and he's days away from his sixtieth. She almost convinces him to stay alive with her, but his daughter begs him to come home, to be buried with her mother, to be surrounded with those who love him when he dies, and he can't do it. Not only does Lwaxana, after all of her raging against it before, go along with it, she goes with him.
Then there's "Darmok", in particular the scene where Picard recounts The Epic of Gilgamesh to the dying Captain Dathon, and with it they finally understand each other.
Data deactivating Lore in "Descent, Part II", even though Lore is a monster.
Lore: I...love you...brother.
The death of Lal, Data's daughter, in "The Offspring"
Lal: I feel...
Data: What do you feel, Lal?
Lal: I love you, father.
Data: I wish I could feel it with you.
Lal: I will feel it for both of us... thank you for my life.
Admiral Haftel, who had been sent to take Lal away, standing in the corridor on the edge of tears talking about how Data had worked so hard and so fast (beyond Haftel's ability to even see what he was doing) to try and save her. He may have been a Jerk Ass to Picard and Data, but he wasn't all bad.
The Expanded Universe novel Star Trek: Immortal Coil examines what happens when Data can feel it. The grief at the deaths of Lal, (by that time) the Juliana Tainer android, and even Lore - never went away, but instead dropped on him like a ton of bricks. As before, he suggests that he should turn off the Emotion Chip to return to his normal efficiency. Picard, as before, talks him out of it, telling him that he has to process his feelings, not hide from them. And he should know.
The closing speech of "Tapestry".
Picard: There are many parts of my youth that I'm not proud of... there were loose threads... untidy parts of me that I would like to remove. But when I pulled on one of those threads... it unraveled the tapestry of my life.
If that weren't enough, Riker then muses about a daring, headstrong, foolish Picard, which opens up Picard to telling stories of his youth.
"Family", whose Fan Nickname is "The Best of Both Worlds Part III", has a few:
Jean-Luc's breakdown after a fight with his brother Robert.
Jean-Luc: You don't know, Robert, you don't know. They took everything I was. They used me to kill and to destroy, and I couldn't stop them! I should have been able to stop them! I tried. I tried so hard. But I wasn't strong enough! I wasn't good enough! I should have been able to stop them. I should, I should.
Robert: So, my brother is a human being after all. This is going to be with you a long time, Jean-Luc. A long time.
To put this into proper context Picard had just come out of a mission where he had been mind-raped by the Borg and turned into one of them in order to not only assimilate him to the Borg but also utilize him and his knowledge of Star Fleet in order to destroy Star Fleet and the very people he'd sworn to protect. One can only imagine the kinds of horrors that he had to endure. One scene in particular is when he is being "upgraded" and a Single Tear falls down his cheek revealing to some degree just how harrowing of an experience it was. This scene effectively shows us what kind of horrors he had to endure to protect not only the people he cared about but Star Fleet and every single citizen belonging to the United Federation
The moment above is enough to quantify as its own Tear Jerker seeing as how Picard is desperately trying to hold on to what remains of his humanity and fight like very few could. Needless to say, both of these scenes are tear-inducing in their humanity and horror.
Jack Crusher's message to Wesley.
Worf's parents concern for his recent discommendation.
Made sadder by the eventual relationship turnout with Lore and Data. Lore did eventually forgive Data, but still ultimately re-programmed him for use of his own ends, and once restored Data was forced to fuse Lore's positronic net, killing him so he wouldn't hurt anyone else.
K'Ehleyr being murdered in "Reunion," with Worf and Alexander arriving just in time to watch her die.
Worf: You have never seen death. (Alexander shakes his head) Then look... and always remember.
There is also how her last moments of life are putting her, Alexander, and Worf's hands together, making sure that, regardless of Worf's discommodation, they have this moment of being truly together.
Let's also not forget the end of the episode, after Worf tells Alexander that he's going to stay with Worf's adopted parents.
Alexander: Are you my father?
Worf: Yes...I am your father.
Years later, in the otherwise average episode "Firstborn," we get a grown-up Alexander's perspective on K'Ehleyr's murder:
Adult Alexander: And then you howled in rage, and said 'Look at her. Look upon death, and always remember.' And I always have.
The ending of ''Lower Decks", especially when Worf sits down with all of Sito's friends to reminisce and mourn her death.
Nurse Ogawa's startled, dismayed gasp on hearing of her death on the com system sells it.
The end of "Silicon Avatar": Dr. Marr has just killed the Crystalline Entity in order to avenge her son Rennie, who was killed by it several years prior. Data, who has many of his journal entries, tells Dr. Marr that Rennie was proud of his mother's career and would have been sad that she'd thrown it away for revenge. This situation plus her expression of remorse... tear-inducing.
Ro Laren talking about her childhood in "Rascals".
Ro Laren talking about the torture and death of her father-while she watched.
In Preemptive Strike, Ro tells Macias this story:
Ro: My father... played the klavion. When I was very young and afraid of monsters under my bed... my father would play for me. He said the sound of the klavion had special powers. Monsters were afraid of it, and they'd disappear whenever they heard it. When I listened to the music he played for me... I was never afraid to go to sleep. When he died I realized... even he couldn't make all the monsters go away.
Tasha's funeral, as she gives a series of goodbyes to all of her friends.
And then there's Data's question after the service:
Data: I find my thoughts are not for Tasha, but for myself. I keep thinking how empty it will be without her presence. Did I miss the point?
Picard: No... no, you didn't, Data. You got it.
The early scene in the Ready Room in "The Most Toys": The Enterprise crew believe Data to be dead, the victim of a shuttle explosion; this scene is filled with Geordi, and even Riker and Picard, trying to fight against the notion that Data is dead. But the clincher, the line that starts the waterworks for me, is from Hamlet, which after Riker has left, Picard reads from his gift to Data, the collected works of Shakespeare: "He was a man, take him for all in all; I shall not look upon his like again."
For me, it was later in the episode, when Worf has been promoted to Data's old post and now sitting in his seat. As they investigate an unexplained occurrence (which, as we all know is business as usual) Picard very casually asks Data for his thoughts on the situation before remembering he's not there anymore. Picard had been handling the situation of Data's death far better than anyone on the ship, but after making this slip-up, in front of the entire bridge crew, you can see from the look on his face how much he really does care.
In "Loud as a Whisper", after the death of Riva's chorus, he suffers a Despair Event Horizon, realising that for the first time in his life, he has no way to communicate with anyone.
The ending of "Who Watches The Watchers": Nuria wishing Picard good journeys and asking him to remember her people is very tear-jerking in a heart-warming way and so moving and so deeply felt... His laconic answer — "Always." — is in the same vein.
Commander Remmick's fate near the end of season one. He's first introduced as a Jerk Ass who is trying to find everything wrong he can with the Enterprise, but only because he was tasked to act that way. After truly finding nothing wrong at all, he expresses his wishes to serve aboard the Enterprise for his next tour of duty. Only for him to unceremoniously be possessed by the mother parasite and blown up in a completely gruesome manner in "Conspiracy."
The fates of Roga Danar and the other Super Soldiers in The Hunted before the Enterprise arrived. They had been genetically modified to be the perfect soldiers, but when peace was declared, they were deemed too dangerous to be around normal people and were institutionalized on the planet's moon.
"Ensign Ro" (Season 5, Episode 3), focusing on the Bajorans. Both the description of their plight - driven out of their home into camps, oppressed, tortured - and the visuals of the camps themselves, and the recognition that this has been the state of affairs for generations and they've had nothing but empty promises to compensate. To anyone who's been to Palestine and to the camps there, much of the episode is physically painful to watch, and the parallels are far too apparent not to appear deliberate.
Anyone who suffers anxiety will relate to Barclay, no more than when he spells out why he's escaping into holodeck fantasies, especially Barclay's last line.
Barclay: You don't know what a struggle this has been for me, Commander.
Geordi: I'd like to help, if I can.
Barclay: Being afraid all the time, of forgetting somebody's name, not knowing what to do with your hands. I mean, I'm the guy who writes down things to remember to say when there's a party. And then when he finally get there, he winds up alone in the corner trying to look comfortable examining a potted plant.
Geordi: You're just shy, Barclay.
Barclay: Just shy. Sounds like nothing serious, doesn't it? You can't know.
It gets revisited in Barclay's second episode, The Nth Degree, where Reg is gifted through Applied Phlebotinum with incredible intelligence, confidence and charisma. This quote makes it a tearjerker moment for him when he returns to 'normal'.
Barclay: Yes, I've finally become the person I've always wanted to be. Do we have to ask why?
In the episode Parallels, the Enterprise from a universe in which the Borg have completely taken over the Alpha quadrant, contact the D to BEG them not to send them back. When they are refused, they choose to attack the Enterprise D of our universe. They know that this alone would destroy them by overloading their weapons, but even this is preferable to returning to that hell. We are so used to seeing the Enterprise fighting with determination and conviction. To see the crew we know and love, all of them, even Riker, driven to the point of desperation and suicide by the Borg, is probably the hardest scene in the episode, if not the entire series in general.
The last lines of the series. Picard, having just finished a game of Timey-Wimey Ball tennis with Q, comes to the weekly poker game for the very first time. He sits down, tells them that he was actually quite the shark in his day, puts the deck down and looks at his friends, with this exchange:
Picard: I should have done this a long time ago.
Troi: You were always welcome.
Picard: So, five-card stud, nothing wild... and the sky's the limit.