This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Pokémon Mystery Dungeon
Red and Blue Rescue Team
The ending of Red/Blue Rescue Team had its sad notes, though not as bad as the following games.
The Red/Blue Rescue Team ending had other characters besides just the partner getting upset at the hero leaving. It's a bit jarring to see Team ACT, who had been willing to hunt you down, getting sad over your disappearance.
The scene where you have to flee town after Gengar claims you're the human from the Ninetales legend may not be as sad as some of the Explorers scenes, but it still manages to be pretty touching. It's mainly because of how Caterpie, Diglett, and Jumpluff all show up to see you off and tell you that they still believe in you.
During the commotion in Pokemon Square, your character is basically unsure if they are the human from the legend, due to their loss of memory. When questioned about it, you can basically say nothing in your defense. Then everyone who views you as a friend starts attacking you. (Lombre even quietly says "Forgive me, Player" before lashing at you.) Then when you run away from there, your partner angrily yells at you demanding why you never said anything. You basically have no other choice but to ask if they should split the team. The brokenhearted look on the partner's face says it all.
A small one set after the ending of Red/Blue: You come back after disappearing, and your partner is so overjoyed to see you... and then a very short while later they basically tell you to stop hogging the position of leader and leaves for their friend area, never to talk to you again except for scripted events.
Explorers of Time, Darkness, and Sky
The pre-credits ending. All of it.
Specifically, The player was really sent back from the future to change the past, knowing full well that saving the world would cause him to vanish from existence. You only learn of this right before Grovyle throws Dusknoir and himself back into the future to prevent Dusknoir from interfering with your task of saving the world. You progress through The Very Definitely Final Dungeon knowing that the player can't reveal his ultimate fate to his most trusted partner, and after saving the world, has only enough time to give his final goodbyes before disappearing into the light and leaving his partner crying from the shock. Out of three Pokémon who left for the Hidden Land, only one returned to tell everyone about it, and it wasn't you. And that's not counting the Really Dead Montage when the partner recalls his memories of their adventures after they arrive on the beach where they first met you, and breaks down crying again alongside Bidoof.
The fact that this was basically the first time we see ourselves talk to our partner, since we only ever see our thoughts and see ourselves 'mime' out decisions to our partner in the game prior. Hearing the good-bye coming straight from the player just made it even sadder.
You: *starts to glow brighter* '...! The light...The light is getting brighter...'
Partner: "D-Don't! Don't...Don't go..."
You: "Thank you for everything, [Partner]. I'm glad we got to train together at the guild...I'm glad we got to go on adventures together...I'm glad...I got to know you [Partner]. "
You: "I'm sorry. I'm so lucky that you were my friend..."
Partner: "I feel the same way! To me, you're...more important than anything..."
You: "Yes...I feel the same way. [Partner]...Even after I disappear from here...I will never forget you... *glows brighter and disappears...*"
Oh, it gets worse: think about how much crap the partner has been through over the course of the game: the Perfect Apple incident, finding out that your idol is a villain, being dragged into the Bad Future for no reason, witnessing the horrors of said bad future, having to deal with the fact that they are the world's last hope for peace… it's a wonder they don't break down earlier.
This music right before the credits of the Explorers games.
The end of Special Episode 2, "Igglybuff The Prodigy". Poor little guy has to watch his exploring master get arrested, not knowing until now Armaldo was a criminal.
Not to mention when Armaldo stopped Igglybuff from attacking Nidoking and Magnezone and then later giving him his Defend Globe before being carried away as Igglybuff cries his eyes out.
After returning from the Miracle Sea, Chatot makes you give up baby Manaphy for its own health and safety, leading to a painful separation.
Especially when Manaphy realises that he has to leave and has to be dragged away by Walrein, screaming your and your partner's names.
The end of Special Episode 5, "In The Future of Darkness". When the flow of time in the future is finally starting to resume, the eternal darkness is finally giving way to a sunrise ... but this also means that since the past is changed, this future will cease to exist any moment. Grovyle, Celebi, and Dusknoir have to fight to stop Primal Dialga from escaping the future, even though they will all soon be erased. Dialga first, Dusknoir second, Grovyle embraces Celebi as they watch the sun rise, with Celebi describing just how beautiful it is to finally see the sun again as the two of them (and everything else) vanishes.
Dusknoir vanishing was especially touching because after spending most of the game hating Grovyle, he thanks him for showing him what it means to live, and that he now has no regrets... *sniffle*
The beginning of Bidoof's Special Episode, with him saying goodbye to his family while sad music plays.
Bidoof's Mama: If you need us, you can always come home.
In that same episode, realizing that Snover and Team Rogue were a bunch of bad guys and they were about to take Bidoof's money from him.
Team Skull's last scene, Chatot's sacrifice and the scene with Wigglytuff afterwards and of course, Grovyle's sacrifice.
The anime version of Grovyle's sacrifice was just as heart-breaking as the game version, if not more.
Grovyle: The future of the world is up to you. Protect the sunrise, for everyone's sake.
When Fake!Cresselia comes and tells you and your partner that you're destroying the world and need to be killed (or kill yourselves) to save it. This can really hit home for those who have felt suicidal in the past.
Although it doesn't touch up on this too much, imagine how Grovyle must feel about the Player Character. His heroic partner, both of you working and fighting hard to save the world. Those two really seemed like a tight nit duo, evidenced during the Dimensional Scream bits when Grovyle praised his partner's good work and when he muses about how to solve puzzles. When those two enter the portal to the past, something terrifying happens, and he begs his partner not to let go. When he wakes up, he's alone with no information to go on as to where his partner is. But he keeps going. And when he finally sees his partner again, neither of them know who they are and they fight each other. Finding out who his partner is, but also hearing that they have no memory of who he is, must be painful for him to process, after all that they've been through. Imagine realizing that you've basically fought your best friend without knowing that they are under a different form, and finding out that they have lost their memories of you.
Gates to Infinity
The death of Hydreigon. Even though he comes back at the very end.
It can also be sad to see your partner's reaction when Kyurem nearly kills you in a No-Holds-Barred Beatdown, with your partner unable to do anything about it.
The Reveal of what the golden orbs the townspeople see are. They're humans that came to the Pokemon world and failed in their mission to save it.
Unlike previous installments, you don't come back post-credits...until you play as the partner to work to bring you back.
Only halfway true, as the first post credits side quest involves bringing your character back for a joyful reunion... unless of course, you choose not to return. One can only wonder how your partner would feel after that...
Narration: Do you want to return to the Pokemon world?
Player: (Is this...the right decision? If I let this chance go now...I don't think I'll ever be able to return to their world again. I would never...see them...again...Wouldn't I...regret that decision?)
Narration: You have no regrets. You will not return. Is this truly how you feel?
Narration: You're certain?
Narration: And so the decision was made...and [Player] made no attempt to go back to the Pokemon world. No regrets. That is how [Player] left the Pokemon world...never to return.
Munna'sMotive Rant concerning their Start of Darkness. All she wanted was to be accepted and to have friends, and all she got was heartbreak and betrayal. Is it any wonder she bought into the Bittercold's promises of a "new, better world"?
Finding out that your partner is an orphan, and has been alone for as long as they can remember, at least until you showed up.
The part before the credits roll when the player breaks down crying. In the English version, the player starts sobbing after hearing the message in the Frism. The dialogue is as follows after the message:
Player: (Sob... [Partner's name]... Even when you said... you wanted me to stay... Even though I promised you...)
Flashback appears. After it ends, it cuts back to the player.
Player: (But... You already knew, didn't you? That I... wouldn't be keeping that promise... That I would have to leave you someday. And... in the end... When our eyes seemed to meet across the sky...)
Player: (Those eyes... The way those eyes fixed on me...)
End of flashback.
Player: (I'm sure of it... [Partner's name]... everyone... You didn't forget about me. You remembered me, didn't you? You looked up at that light, knowing it was me... to say goodbye... You even managed to overcome your fate to forget me... [Partner's name] still... Everyone still... They still remember me... [Partner's name]... My... friends... Sob...)
In the post-game, whenever the partner wakes up and sees the empty patch of hay where the player character would have been sleeping at, every single morning.
Especially as it's pretty strongly implied that your partner is suffering from depression. The fact that he resolutely becomes a Stepford Smiler does not help at all.
What's worse is the animation: the partner wakes up and immediately turns to the empty bed, just like they used to when the player was still around. It's like they're hoping that it's just a dream and one day they'll wake up and find that the player never left.
Despite missing the player greatly, the partner was actually willing to sacrifice a chance to see the player again because they knows that the player had friends and family back in the human world who must have been worried sick about where the heck the player was and they didn't want them to suffer from the player's disappearance and who knows if the player is actually willing to be separated from their friends and family in the human world forever. They fear that if the player comes back that there might be a chance the player might never be able to return to the human world. They were willing to continue on their own suffering just so the player won't be separated from their love ones. Fortunately this issue was resolved by having the player granted the ability to travel between the two worlds thus the player didn't have to hurt anyone.
Super Mystery Dungeon
Very early in the game, after your partner leaves Goomy behind in the dungeon, your partner starts to wonder if they're annoying. They ask you and regardless of what you say, they will become upset and they will not talk to you for a bit. The next day, they will not ask you to walk to school with them because they don't want to be irritating.
Budew went to the Beedrill and Combee to gather Honey because her mother was sick and she hoped it would cure her illness.
Telling your partner you have to leave Serene Village is pretty heartbreaking. Your partner understands that you want to protect everyone, but they clearly do not want to lose the only friend they have. Subverted though, when they decide to come along with you anyway.
Before you leave Serene Village, with your partner, you are stopped by Deerling, Goomy, Espurr, Shelmet, and even PANCHAM. They all want to say their goodbyes. If that's not sad enough, its revealed that Espurr told the adults and they accept the fact that you are leaving the town. All of the major characters in the town leave you heartfelt letters, including ones from Carracosta and Nuzleaf.
Someone who is closest to a father figure as it comes, turns out to be manipulating you to do what he wants the whole time. Of course we then find out that he was under the control of Dark Matter. But he still can't bring himself to show his face to you, whether if you forgive him or not.
The ending has yet another sad goodbye scene. This time, you're the one left heartbroken, as you watch your partner fade away.
And then the credits roll with super-dramatic music as you stand under the big tree alone, crying over your partner's absence.
The whole ending is made even worse when the credits roll and you see the lateSatoru Iwata in the credits, making this one of the final games he was an Executive Producer for before his death.
If you take Mew to Serene Village before Purifying Cave, everyone will comment on your new friend but what really makes it sad is that Carracosta accidentally mistakes him for your Partner. And when he realizes he isn't he shakes his head sadly saying that he's seeing things. He really misses his kid.
Mawile and the Legendary Beasts' Heroic Sacrifice. The escape point is mere inches from them, but they choose to stay behind and fight against hopeless odds just so you and the Partner have a chance to escape. Ampharos is absolutely crushed that his lifelong friend and partner is gone, which explains why he's so pissed when you confront Nuzleaf again. Especially poignant as, since Mawile was no doubt defeated by the Voidlands Shades, there was no guarantee that her soul would return to her body once Dark Matter's petrification was undone.
Have a Legendary Pokemon as one of your favorites? That won't save them from being turned into stone and essentially dying which can be dispiriting if they are among those that are killed on screen. The Lati twins may have the worst death; a close look at the way their statue's arms are spread out and angled implies that the two siblings were trying to hug each other as they die, or even trying to push each other out of the way of the villain's attack only for both of them to become petrified. After being separated during the events of the first game, it wouldn't be a stretch that they were completely desperate to protect each other and not lose each other again.