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Tear Jerker: Planetes
The episode of Planetes where we find out why Yuri became a debris collector.
The conclusion of episode 7: "Extraterrestrial Girl". "This is my ocean."
Gigalt, about Hakim, shortly before dying. "Why...? Why couldn't I think of one for him? Why couldn't I come up with a nickname...?"
The end of the series when Ai, who has been carrying an injured Claire - who she knows is a terrorist - cross-country over the moon and she sees the lights of the dome just as she runs out of air and she screams.
There was also the glorious subversion in Planetes. After the Wham Episode "Love," and the equally powerful episode 25, Hachimaki and Ai have returned to Section 7 for one last tour, the latter having recovered from her severe injuries. As they stand on the hull of the Toy Box, they begin a word game, naming objects that start with a specific letter. This is how Hachimakiproposes to Tanabe.