During the first fight against the Borg, the Borg adapt to the Starfleet phasers rather quickly. Worf's "Captain, they've adapted!" would sound slightly fearful when said by a member of any other species. Worf? Hell no. He takes his rifle and starts clubbing the Borg drones with it.
Picard is going blind with revenge against the Borg and calls Worf a coward for falling back and destroying the Enterprise. Worf stands up to him, face to face, and says with as much restraint a Klingon can have, "If you were any other man I would kill you where you stand!"
Another for Picard and his effect on Worf — there are precisely two men in the universe that Worf would let insult him like that without violent retribution. One is his son Alexander. The other is Picard.
While this troper feels the entire film is one long crowning moment of awesome, special notice given to the period from when the the Phoenix launches (complete with its own Crowning Music of Awesome) and flies away from the Earth with the Enterprise in pursuit, while at the same time Picard looks utterly screwed ... until suddenly Data reveals his hand and breaches the coolant tank.
The Phoenix has another CMoA as it reaches orbit. At first it just looks like this rickety, cobbled-together thing that's barely a step up from a 60's space capsule... Then the side panels come off, and slowly a pair of Star Trek-style warp engines unfold and lock into position. And that is when the discerning Trekkie knows epic-ness is about to ensue.
Another for both Zefram Cochrane and Steppenwolf: Cochrane launches his modified nuclear missile to go to warp flight and get the attention of the Vulcans, leading to Earth's first contact with an alien race ... and he does it while blasting "Magic Carpet Ride" across the whole base.
First Contact itself, especially as the aliens are revealed to be Vulcans.