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Tear Jerker: Sgt. Frog
The Season One Finale (and the manga equivalent, "The World's Smallest Invasion") is probably one of the biggest. It would be hard to come up with a more painful way to retouch upon everything shown in prior episodes.
Of special note is when Dororo and Koyuki say good-bye. Koyuki has been the only true friend of Dororo's and the only one who's never forgotten him, and now he must say good-bye. Their hug seals the deal.
Even after that, there's the scene where Fuyuki discovers a model kit that Keroro left behind after the platoon left Earth. Fuyuki doesn't have his memories of Keroro any more but upon looking at the box he feels like something's missing and starts crying. This part's such a tearjerker that Funimation's Gag Dub of the series, which otherwise changed the dialogue up to add humor in even in moments that were supposed to be more emotional, completely played this scene straight.
The first movie, all the human/Keronian partners breaking up and everyone's subsequent reactions. *sniffle*
Keroro and Alternate Universe Fuyuki parting ways in episode 205. A surprisingly, and rather strikingly good, tearjerker moment.
The ending of episode 262 has the potential to start waterworks too. We have Keroro hurrying to the station to catch his mother before she leaves on her flight home, to apologize to her for hurting her feelings. He doesn't get there in time.
The Season Two Finale with the Garuru Platoon. The rest of the Platoon's been taken out and Keroro's now Brainwashed and Crazy and ready to take over the Earth. Fuyuki runs up to him and begs for him to stop, screaming for him to come to his senses. It works.
Episode 284. It's truly moving. When a new commander comes and put forward an extremly evil plan, Dororo is forced to resign from Keroro platoon. Then he doesn't tell anyone and suffers everything alone. But when the plan goes wrong and his teammates are in danger, it is Dororo who saves them.
Movie 5 where everyone reacts to Keroro's death, especially Giroro. He is the only one to speak his name and suddenly starts running to the site of the explosion, even in his weakened form, screaming his name. It gets even worse when after Aku Aku descends to confirm Keroro's death and leaves after mocking him how pathetic and useless he died, Giroro screams to the sky in grief.