Star Trek VI gave Kirk a few sweet moments: who can forget his triumphant "Fire!"? And then there's this remarkably cold blooded exchange:
Spock: Jim, there is a historic opportunity here.
Kirk: Don't believe them. Don't trust them.
Spock: They're dying.
Kirk:Let them die!
Although according to William Shatner's Star Trek Movie Memories, this wasn't how Shatner had intended the line to come off. As it is, the unedited shot includes Kirk physically recoiling, to provide the impression Kirk had regretted saying something so bloodthirsty. Nicholas Meyer, the director, promised Shatner he'd leave the full shot in. Guess who's still waiting.
Also, one might call a Values Dissonance on how awesome that moment is due to it showing us that Kirk can't (for the moment) let go of his ill will toward all Klingons, when only one was truly responsible for David's death.
Also, the very end of the film, Captain Sulu bringing in the cavalry. "Fly her apart, then!", not to mention "Target that explosion and fire." when he arrives. It's the closest you ever get to Sulu saying "That guy, ruin his shit." The man has a half-dozen lines and barely a minute of screen-time in the film and he still manages to be an equal badass to Kirk. As stated elsewhere on this wiki, many of Kirk's crew closed out their careers ranked as captains, but only Sulu became a Captain.
Sulu gets his awesomeness in from his very first scene, where Captain Sulu calmly sips his tea on the bridge of his ship, with the smuggest grin imaginable on his face.
Also, steering Excelsior into the Praxis shockwave and allowing the ship to ride it out. Awesome.
Scotty kicking a metal door down and phasering the "Klingon" sniper.
The Klingon ambassador applauding Kirk's speech, after having called for his head both earlier in this movie and in Star Trek IV.