For a series that is, basically, about garbage men, Planetes had more than its share of awesome:
After being denied a good, long smoke for a very long time (oxygen is a commodity inside a space station, after all) and being thwarted by everything from automatic sprinkler systems to an actual terrorist attack, Fee Carmichel, captain of the Toy Box, sees that the terrorist organization Space Defense Front is about to ram a rogue satellite into the station which houses the last available Smoking Room. She then helms her ship at full thrust and rams it head-on to the satellite, causing it (and herself) to plummet harmlessly into the atmosphere, leaving the station's crew in utter awe and admiration at her "noble sacrifice." The fact that she had saved the entire planet from a devastating Kessler Syndrome hadn't even occurred to her, all she wanted was revenge for being denied her smokes... which she finally got, drifting at sea on her inflatable raft (the fact that she survived and used her emergency pod was a miracle in itself.)
Everything Hachi does during the Von Braun crew selection trials, but especially his EVA tests.
Hachimaki confronting Hakim for betraying his trust and trying to sabotage the mission is a favorite.
Anime only: Ai Tanabe's unbelievable sacrifice in order to save Claire from suffocating when stranded on the surface of the Moon. More poignant because, all throughout the series, Ai's ideals of love had been mocked left and right by everyone in the cast, but Claire herself had ripped into her viciously and mercilessly. In the end, although she survived (but with severe nerve damage,) Ai proved that she was willing to live up to her ideals to the ultimate consequence.
At least, for this troper, what really clinched the series for him and made him want to watch the rest of it was Ai Tanabe's amazingly passionate, and well-performed speech (might I even say Hot-Blooded?)in episode three, accompanied by a rising, deep male-voiced chorus. Beyond epic.
Every single thing Werner Locksmith says or does. Ever.
Everyone in Episode 18, but especially Edel and Chief. Chief tackling the asshole division director, and Edel beating the crap out of the security agents.
Everybody in Debris Section gets one, even the clerk staff.
Hachimaki's EVA tests deserve special mention. This troper cried when he saw it the first time.
Werner Locksmith, satisfied with the test results from the moon incident. Even the characters were floored.