Taking Implacable ManUp to Eleven when Uhura is trying to stun him with a phaser. He takes ten, maybe eleven shots, and each just shoves him back a bit before he goes right back to trying to close in on her with a bloodchilling Death Glare. The look on Uhura's face is sheer terror as she realizes that all she's doing is slowing him down and pissing him off.
If he's not actually doing something, you can just tell he's plotting. Not thinking. Plotting.
As a crewmember, it would be bad enough being sucked out into space when the hull's breached: Now imagine being one of the casualties when the Vengeance blows holes in the Enterprisewhile they're at warp.
The Vengeance itself is pretty terrifying just when they reveal that it can actually catch up to the Enterprise in warp, and we can just see it bearing down on the Enterprise with the creepiest of noises. Not to mention that it looks very intimidating, courtesy of its black paintjob and massive size.
Spock going berserk and almost beating Harrison/Khan to death.
The scariest part is we had just seen both Khan and Spock in an intellectual battle; not civilized, but cool, calm and in control. Then Khan thinks Spock killed his family, and Spock witnesses the death of his best friend and all bets are off. Their intelligence and control are completely gone.
Khan was terrifying because we knew what he could do and we finally got to see it completely let loose. Spock was terrifying because we have never seen him go full-blown on someone before this moment. And holy shit can that Vulcan do damage! He attacks Khan with the nerve pinch, and breaks Khan's arm over his shoulder after hitting him repeatedly with a piece of metal he tore off the vehicle they were on!
Pretty much any of the screams in various points of the movie (the screams following the data archive in London being blown up, the screaming of the Enterprise's crew being sucked out through the hull breach or when several are caught in another explosion, Carol's scream upon witnessing Khan crushing her father's skull).
Admiral Marcus forcefully having his own daughter beamed off the Enterprise so that he can destroy it without harming her. Carol's screaming while she's being beamed off makes the entire scene even more chilling.
Adult Fear at its finest: The death of Admiral Pike. He's obviously afraid and in pain, and despite Spock's efforts, he dies that way.
Likewise, Kirk's death. Imagine being in Spock's place: watching your best friend slowly die from radiation poisoning, while being completely helpless to do anything to save, or even comfort him.
Khan crashing what's left of the Vengeance into San Francisco. Considering the number of buildings felled, it's like 9/11Up to Eleven. Likely many thousands of deaths.
When Bones gets his arm trapped in the torpedo. Think about it from Kirk's point of view—he can't beam Bones back aboard without taking the torpedo with, and if he beams Carol out then he's condemning his best friend to certain death. At the same time, if he let her stay and she couldn't defuse the torpedo, they're both dead. Imagine having to make that choice.
What's worse is how fast he has to make that choice. It all happens in 30 seconds!
The scene where the Enterprise is falling into Earth's atmosphere.People are falling through the ship's levels, and they're either crashing into things like walls, ramps, and well, THINGS. Or having things fall on them. Imagine hanging on for dear life and something - or someone - smashes into you. Yikes.
It gets worse. We get a quick shot of the shuttle bay, with shuttles getting tossed around like toy cars while the crew is attempting to Abandon Ship. They can't even escape while the ship is tumbling like that. Even Starship Troopers didn't have as unnerving a Sinking Ship Scenario as this film pulls off.