This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Pokemon Games
The final battle with Red in Generation 2 (And its remakes) is uncharacteristically poignant for the series. No words, not even a flashy departure. When you beat him, his whiting out and scurrying off to the nearest Pokémon Center will bring tears to your eyes.
In a rarely-noticed bit of Fridge Horror, the realization regarding your rival in Pokémon Red and Blue. You see him in the Pokémon Tower in Lavender Town, and he asks you if you're there visiting a dead Pokémon. Last time you fought him, he had his Raticate, which you likely swiftly defeated and which he no longer has in his party. Now, this isn't to say that you're necessarily to blame...but keep in mind this is Red/Blue.
The ending for Grovyle's special episode in Sky. Oh. My. God. The Delayed Ripple Effect catches up with them as Primal Dialga is defeated, the world starts growing brighter as time begins moving again. Dusknoir vanishes while asking if his soul shined, and then Grovyle and Celebi watch the sunrise together as they too begin to vanish from history.
The ending to the game where your main Pokémon fades out of existence by restoring the timeline, and right before the credits, your partner breaks down and cries in front of Bidoof. This was so moving that even Dialga felt their pain, and brought your main Pokémon back into existence.
The music and the dialog makes this scene even harder to watch.
The ending to Igglybuff the Prodigy was definitely a big one, too. Poor master Armaldo.
The resolution of the story between Gengar and Gardevoir in the first game.
The anime adaptation of the scene only makes it even more heart wrenching. "I'll leave it to you to protect... this world's beautiful mornings."
The true tear-jerking moment began when Grovyle said:"And Chimchar! You take good care of Piplup!" Chimchar: "But I can't do what you can do!" Grovyle: "You'll do just great!" He begins to fall towards the portal. "You two are a great team, and don't you ever forget it!". He falls into the portal. Right before he enters, he says: "The future of the world is in your hands. Protect the sunrise... for everyone's sake."
"I am, up to the very end, not wavering, honestly. I lived because of you Grovyle. Thanks to you I have no regrets."
The very first Pokémon generation, as well as their remakes, include the Lavender Town plot. The Lavender Town music is slow and kinda sad on its own, and its biggest feature is Pokémon Tower, a graveyard for departed Pokémon. That's not why the town's plot is so heartbreaking. Apparently, Team Rocket tried to capture a rare Cubone, but its mother saved it - and the Rockets killed her. You actually meet both the little Cubone and the vengeful spirit of mama Marowak... and it's up to the player to calm her spirit by facing her in battle. Mr. Fuji is praying alone for Marowak's spirit...
While it's common knowledge now, fighting through a game that can take 120+ hours to beat and finding The first game's protagonist isolated and alone at the very end was a kick in the face.