This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Mystery Science Theater 3000
There's something oddly sad about the show's closing theme. It's a slower-paced version with an emphasis on regal-sounding brass, as though it's some sort of wedding or funeral procession, until about halfway through when the rest of the "ensemble" kicks in with a nearly heavenly sound before closing with the familiar "twang" of the original theme. Especialy if you're a fan of the show, it's likely to bring a tear to your eye.
In the final episode ("Danger: Diabolik"), while using a joystick to control the Satellite of Love, Pearl accidentally breaks the control and sends the SOL spiraling down to earth. Realizing that all of her experiments have failed, and there's no way to continue, she has a massive Villainous Breakdown, throwing her rage around the castle. When we cut back to her, her mascara has streaked down her face in tears, and the actress playing her really does look like she's upset about the series ending.
Word of God: Both Mary Jo Pehl and the rest of the crew all confirmed that she was hit the hardest by the cancellation. She also did the final ever filmed scene of the series, when she (cruelly) is forced to tell Mike and the bots, "Look, Nelson, MOVE ON. I have."
The final shot of Mike, Crow and Servo riffing a bad movie, this time at home, with no one forcing them to. Stockholm Syndrome? Maybe, but Word of God said that they were simply emulating what everyone does during a bad movie. And of course, realizing it's over.
Gypsy at least becomes the CEO of ConGypsCo. Mike and the 'bots were offered shares, they passednote Crow: If you recall, I made a fart noise, which she only took as a "no"., which is why they're living in a the basement apartment of an efficiency in Wisconsin. They still think it's "sweet living".note Well, it is right on the bus line.
Despite the disturbing lyrics, Forrester's "Who Will I Kill?" song after Frank ascended into Second Banana Heaven is a huge one.
Basically, any time Joel, Mike and the bots come close to being utterly broken by a film. Examples include Manos, Hobgoblins, Red Zone Cuba, Invasion of the Neptune Men, Monster a Go-Go, and the most severe example of the film nearly breaking them, Castle of Fu Manchu.
The short "Catching Trouble", about a man named Ross who hunts down and captures wild animals for zoos and to sell as exotic pets. Seeing the animals crying out in fear as Ross manhandles them, throws them into sacks, and drags them away from their homes is really heart-wrenching, even with riffing.
In the final host segment of Santa Claus, Mike exits the theater alone and starts singing I'll Be Home For Christmas softly to himself. This was not too long after Mike had been trapped in space and in that moment you realize the reality of being away from his family during the holidays is really getting to him.
Servo's song from "Gamera", Tibby, Oh Tibby, though played for laughs, can come across as incredibly sweet and heart wrenching, especially to those who have had pets pass away.
Servo, playing with his bow and arrow, accidentally shoots a baby satellite. Despite the silliness of the sketch's premise, Servo's dialogue and acting are an extremely realistic depiction of a child's regret and sorrow after making such a mistake. The satellite somehow manages to be a Ridiculously Cute Critter despite being nothing more than an object, and its mother coming to reclaim it is a majestic Heartwarming Moment.
Servo's head explodes in Star Force: Fugitive Alien II, but this time it's a serious, critical injury. Joel's despair is pretty sad during the host segment.
Crow and Servo both wind up being incredibly depressed after the Downer Ending of The Sidehackers. Even the song Joel sings is pretty melancholy.
The end of Danger! Death Ray has the protagonist destroying several cameras, which drives Cambot into actual tears. Crow and Tom proceeding to call him a baby doesn't help.
The "Clown in the Sky" song from the closing host segment for Pod People is really quite melancholy (aside from Joel getting angry at Tom Servo's Anthony Newley impression, and the Mads' reaction of "It stinks!").
Kinga Forrester gets quite an Alas, Poor Villain treatment when it turns out her grandmother barely seems to acknowledge her existence and her restarting the experiments suddenly looks like just her latest desperate attempt for approval. She's driven to tears within a couple minutes of still failing to get a positive response.
She gets another one when Neville, a magician she was conversing with, decides not to meet her physically, saying he loves her to do that. It doesn't help that it shows that Max is in love with Kinga as well.
The guys are all quite disturbed by the unusually drawn-out and realistic death of the monster in Yongary, asking if Werner Herzog directed it. They end up doing a whole song about the feeling of just having seen a movie with such a scene, and being unable to stop thinking about it. Even Kinga and Max are upset about it and wonder if they should turn away from their evil ways... for a few seconds, anyway.
Jonah getting (possibly) killed at the end of At The Earth's Core. Joel and Mike were eventually able to escape captivity and return to their normal lives, but not Jonah.