This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / The X-Files
"Conduit" offers us a pretty melancholy ending, with Mulder sitting in an empty church at night, gazing at a picture of him and his sister as children. He then breaks down crying, thinking about how much he wants to find her. As this is happening, we hear a tape recorder playing one of his sessions with a hypnotic therapist. It's Mark Snow's score that really helps accentuate Mulder's loss. The sounds of the flute and synthesizer are gently building as we hear more of Mulder's recorded interview with a therapist.
Therapist: Can you see your sister?
Mulder: No. But I can hear her.
Therapist: What is she saying?
Mulder: She's calling out my name... over and over again. She's crying out for help, but I can't help her. I can't move.
Therapist: Are you scared?
Mulder: I know I should be, but I'm not.
Therapist: Do you know why?
Mulder: Because of the voice.
Therapist: The voice?
Mulder:The voice in my head.
Therapist: What's it telling you?
Mulder: Not to be afraid. It's telling me that no harm will come to her, and that one day she'll return.
The episode "Roland" was heartrending, especially the end where Roland leaves his home and gives Tracy his jar with the stars. Horrible that they like each other so much and must be separated.
Scully's storyline in "Beyond the Sea" is heartbreaking, having her dealing with losing her beloved father. Especially her ending lines, "He was my father."
Deep Throat's death in "The Erlenmyer Flask". He's shot in cold blood while bartering for Mulder's life, and dies in Scully's arms.
"Trust no one."
Duane Barry, while far from the cuddliest of figures, is put through so much pain that one can't help but feel for him in a Jerk Ass Woobie kind of way.
Whenever Scully breaks up and is Not So Stoic, chances are it's going to be a Tear Jerker. Just look at the ending of "Irresistible". She is always such a strong and capable woman, and very hard on herself. When she finally let Mulder comfort her...
Mulder while Scully is abducted. He just loses it. In "3", he's offered a hotel room while investigating a case out of state. His response? "I don't sleep anymore."
When Mulder thinks that he's lost Samantha again in "End Game", particularly for the scene where he confesses his mistake to his father. Mulder is uncharacteristically in tears while retelling what happened, and his father is nothing but cold, noting how negatively this will affect Fox's mother.
In "End Game" when Mulder is knocked out by the bounty hunter and wakes up to find all of the clones missing, right after they had asked for his help.
The deaths of several of the family members in "The Calusari", while primarily Nightmare Fuel, also tread into this territory. Teddy's in particular, for epitomizing every parent's Adult Fear. Also, Steve's, due to Charlie shouting out for him while locked in the garage car, showing to us that the deaths are not entirely his doing.
The final fate of Dr. Banton in "Soft Light", who, after spending the entire episode in torment and wishing for death so that he can avoid hurting others, ends up being used as a figure for experiments in a government research facility. He even can be seen letting out a Single Tear in the final shot of the episode. Additionally, Banton was forced to kill Detective Ryan before this (affecting Scully in a very hard way), which makes his ultimate ending a huge case of Shoot the Shaggy Dog.
The death of Mulder's father in the season finale, right after he had started to atone for his earlier work. His last words are to ask Mulder to forgive him for his mistakes.
The end of "Paper Clip" — Scully finds out her sister has died.
"D.P.O." has a bit of this when we see Zero (played by Jack Black) begging for his life, just before getting blasted by Oswald's lightning.
"Clyde Bruckman's Final Repose": Mr Bruckman's ultimate fate. After life seeing deaths, at times extremely gruesome, he felt Driven to Suicide.
From "2Shy", there's Jesse's reaction after realizing that her mother has been killed in Virgil Incanto's apartment. Further exemplified with her later discussion with Scully.
"The Walk" deals both with the troubles that some Army veterans have trouble returning home from war (sometimes, if not often, feeling underserved by the Army that should ostensibly be helping them to recover). On the other side, several of Rappo's actions to take vengeance are pretty cruel , as seen with what happens to General Callahan's family.
Much of the pain we see Skinner go through in "Avatar", from being accused of murdering a woman he slept with, to the conversations he shares with his estranged wife.
The death of Queequeg in "Quagmire". During the next scene, Scully is seen fighting back tears and barely listening to Mulder as he gives one of his exposition dumps. Made all the sadder, seeing as how it was a parting gift from Clyde Bruckman, and she named it that because Scully's father often read Moby Dick to her as a child.
"Wetwired": Mulder's distress when he's about to identify body that could be Scully. Even though it's something of an Audience Reaction of Like You Would Really Do It, his emotions are genuine.
"Memento Mori" is the episode where Scully's cancer is diagnosed. It is a direct and shameless heartstring-twister from start to finish. It works.
All of "Kaddish", especially the story behind the wedding ring. Poor couple, they could have been so happy together.
"Musings of a Cigarette-Smoking Man", unreliable narrator aside, does little to dissuade the audience from believing that the CSM really does have little happiness in his life.
The ending of "Elegy," with Scully crying alone in her car.
In "Gethsemane," after having been told his quest is a lie and losing his proof of alien existence, the cherry on top is that those conspirators behind the aforementioned devastations gave Scully her terminal cancer only so he'd believe the lies they fed to him. The way they order those revelations, one could assume Scully's ailment was the tipping point of his suicidal thoughts.
The scene in "Redux II" where Scully tries to get Mulder to pin the death of a man he killed on her — because she doesn't want him to go to prison, and she's going to die soon anyway. The look on Mulder's face is just heartbreaking.
In "Redux II", Mulder sobbing at Scully's bedside while she sleeps.
The ending of the episode "The Post-Modern Prometheus". The whole scene works on two levels and depends on how one interprets the writing. It feels very heart-warming, but considering that it's what Mulder told the writers (the boy who wrote the comic or even the writers of the show — very appropriate for Postmodernism) to appeal for a better ending, it might very well be just something what he wishes to happen for the monster and for himself. Which makes it more of a truly tear-jerking moment.
The last twenty minutes of "Emily".
The transition from Scully's laying with Emily to Emily's funeral was especially hard on this troper. The imagery of Scully laying with her dying daughter while the stained glass of the chapel portrays the Virgin Mary with her (living) son and Bill's newborn daughter in his wife's arms probably helped absolutely nothing.
The ending to "The Unusual Suspects." After the Lone Gunmen solidify into a trio, and go after the attempt to poison unsuspecting asthma patients with a mind control drug, things go to hell in short order - the warehouse is shot up, the drugs vanish, the trio are arrested, and the last they see of Suzanne Modeski is her being shoved into a car and kidnapped in broad daylight after she tells them "no matter how paranoid you are, you are't paranoid enough." It's especially harsh on Byers, who saw every part of his worldview wrecked in the process.
"The Unnatural", baseball, fun-loving aliens, the gospel and song and finally It's just blood. The death of the alien who made such a good human is very heart-wrenching.
In "Monday", after Mulder was shot, Scully pleading with Bernard to let her leave with him. Made even more tear jerking because of the wounded look on her face, and the fact that she's near tears as she tries to stop Mulder's bleeding.
"Three of a Kind" opens and closes with them. In the first, is Byers's Tragic Dream. He's a Wide-Eyed Idealist and possibly the most moral man in that universe's canon. His dream is of a world where the country he loves lives up to the Type 1 Eagleland, where he has a comfortable middle class existence with the woman he loves and two adorable little daughters...but then it cuts to him standing in a vast desert, holding a wedding ring, all alone. And at the end? Well, Suzanne is safe and going off into a new life, but they'll likely never see one another again. And Byers is holding a wedding ring, out in the desert as she leaves.
The episode "Trustno1", especially the e-mails between Mulder and Scully — poor Mulder just wants to come home.
The ending of "Release", with Doggett and his wife spreading their son's ashes into the ocean.
When Doggett's amnesia in "John Doe" gets broken by the memory of his murdered son. It's the one of the few times we ever see him cry.
Doggett breaking down in "Audrey Pauley" begging the episode's namesake to go into the spirit world and have Reyes give them a sign she is alive.
Reyes taking Doggett off life support in "4-D". Thankfully, it was a Doggett from a dimensional rift that was restored when he died.
The end of "Jump The Shark" for fans of The Lone Gunmen with their deaths.
The end of "William" when Scully breaks down over William's crib realising that she has to give him up to keep him safe.
In the first episode, "My Struggle", it's revealed that Mulder and Scully have broken up and become estranged, and both are now more or less completely alone.
In "Founder's Mutation", Mulder and Scully discuss William, with Scully admitting that she hates herself for giving him up, while Mulder says that he's "put that behind [him]". Except it turns out Mulder hasn't put it behind him—both he and Scully still keep photos of William with them and fantasize about raising him.
Said fantasies are themselves a mix of tearjerker and Nightmare Fuel. They start out happy and benign, only to get darker as Scully's and Mulder's personal fears take over. Scully's fantasy ends with William undergoing an alien mutation like Emily did, while Mulder's ends with William being abducted in exactly the manner Samantha was.
Large portions of "Home Again", which deals with the heart attack and death of Margaret Scully.
When Scully gets to the hospital, a nurse tells her that her mother was asking for "Charlie" (the youngest Scully child and who had apparently become estranged from Margaret). Not Bill (her favorite) and not Dana, not any of her grandchildren, but Charlie.
Scully's speech to her unconscious mother:
Scully: Hi Mom, it's me Dana. I'm here. I've been where you are. I know that Ahab is there, and Melissa. But I'm here, Mom. Bill Junior's here. And William - William's here. Please Mom, don't go home yet. I need you.
Margaret's last words being to her missing grandson William, and Scully's reaction:
Scully: (crying) Her last words to us were about our child, her grandchild, that we gave away. Why did she say that? Why did she have to say that?