Right when the Enterprise is about to warp to Genesis, Excelsior Captain Styles gives Kirk an ultimatum: "Kirk, you do this, you'll never sit in the captain's chair again". Kirk's response?: "Warp Speed". Kirk was willing to end his very career right then and there (effectively resigning from Starfleet) to save his best friend.
Once again, Shatner proves He Really Can Act. You see that he knows exactly what this will likely cost him, that moment where he decides that Spock is more important to him than everything his life had stood for up until that point.
Those chugging noises... [giggle] when the Excelsior's transwarp drive malfunctions.
Kruge calling Kirk on a bluff, the only time it's been seen in any Kirk era story.
The original Enterprise, in her last moments, takes down half a dozen Klingons with it.
Torg: My lord, the ship appears to be deserted. Kruge: How can that be? They're hiding! Torg: Yes, sir. The ship appears to be run by computer. It is the only thing that is speaking. Kruge: Speaking? Let me hear it. Enterprise computer:[Torg holds his communicator to it] 9...8...7...6...5... Kruge:GET OUT! GET OUT OF THERE! GET OUT! Enterprise computer: 2...1... [the Enterprise bridge explodes]
T'Lar: What you seek has not been done since ages past—and then, only in legend. Your request is not logical. Sarek: Forgive me, T'Lar. My logic is... uncertain, where my son is concerned.
Kirk and Sarek after the re-fusion ceremony:
Sarek: Kirk, I thank you. What you have done is... Kirk: What I have done... I had to do. Sarek: But at what cost? Your ship. Your son. Kirk: If I hadn't tried, the cost would have been my soul.
Spock when his Katra is restored.
"The needs of the one outweigh the needs of the many."
Let's not forget how he easily dispatched the much bigger guard, or how he casually blasted away at the control panel with a delighted look on his face.
This one deserves a CMOA on a meta level as well, since George Takei was opposed to the scene where Sulu is called 'Tiny'. It wasn't until he saw the finished print that he finally admitted that the scene was one of Sulu's finest moments.
Uhura's part in the plan—she takes a posting at an out of the way transporter station, paired with an obnoxious young officer, then, when Kirk and company enter, she pulls a phaser on "Mr. Adventure" and makes him get in the closet.
Like the above instance with George Takei, Nichelle Nichols was initially upset at how little she had in the script until she actually read the part and loved what she got to do with that little.
Given the time and circumstances in which the original TV show existed, Uhura was intrinsically awesome just by being an indispensable crew member on the bridge who happened to be a black woman. Whoopi Goldberg cites seeing Uhura on TV as a life-changing moment for her—and that was undoubtedly echoed in the minds of millions of other young people at the time. Giving her a bad-ass action moment here may have been long overdue, but it comes as no surprise that she's more than capable of handling herself.
According to the novelization, once she'd beamed Kirk and Co. aboard, she immediately transported herself off, fled to Earth with Starfleet Security half-a-heartbeat behind, showed up at the gate to the Vulcan Embassy, and got Sarek to grant her asylum status before she could be captured and taken back.
The Reveal of the Excelsior. Her first time out of the gate might've been an Epic Fail, but she would go on to be a vital part of the Trekiverse, not to mention one of Starfleet's most utilized designs.
Scotty getting promoted to the rank of Captain of Engineering. Sure, other non-command division people in the various series eventually became captains, but they all did it by getting command of a starship. Scotty is instead promoted because he's just that badass of an engineer.