The ultimate, but less obvious, scary scene is a scene that is unwatchable as an adult. It's the scene where Nemo has been taken, and Marlin is desperately rushing around to find him, only to see empty ocean- all while screaming his son's name.
The music during that scene doesn't help matters, either.
The barracuda that kills Marlin's family in the beginning.
The barracuda just hanging there in the water silently waiting to strike was pretty terrifying too. If you know anything about them they're torpedoes with razor-sharp teeth.
Torpedoes, indeed. How do they first notice it? When it took out their entire neighborhood without them even noticing until long after, greeted with a dead silence the next time they look at it.
A good way of showing this; the barracuda, upon first being seen, is just... observing them in the most frightening way possible. Then, Coral makes a blind move, and literally five seconds later, she's dead with her husband knocked out.
The nightmarishness of this scene is mentioned in The Simpsons. Milhouse's mother always skips it for him, and he ends up absolutely terrified when he accidentally discovers it on his own.
It is scary enough to look at with all those teeth, but it's also a particularly aggressive hunter, especially after Marlin. Later Played for Laughs considering how distracted and bubbleheaded Dory is acting, fully oblivious to how close to danger Marlin is as she tries to read the address on the diver's goggles in the ravine.
In the DVD commentary, they mentioned that after a preview, they considered lowering the volume of the anglerfish (or just getting rid of its screech altogether), but a young kid turned to them and said that "tuning down the anglerfish is like tuning down nature itself". Still, it's frightening in surround-sound.
Marlin finding Dory tangled and looking dead in the tentacles of a jellyfish. Not to mention her wounds afterwards from being stung so badly and the Fridge Horror that if Marlin hadn't gotten her out of there, she would have been Eaten Alive.
Darla. Especially once we first see her. You know - in a picture holding a dead goldfish. It would be a lot more scary if Nemo wasn't terrified to be her next victim.
Darla:Fishy? (Roughly shakes the bag with Nemo in it) FISHY!? Why are you sleeping!?
She even has her own Scare Chord for when she finally arrives.
And not just any scare chord, they brought out genuine Psycho Strings for her.
Imagine being in that bag, knowing that if someone doesn't make her stop, and quickly, you're a goner. And there's not a damn thing you can do about it.
Any shot of the sea when it isn't bright and friendly is pretty scary, especially to aquaphobics. Take Bruce's den with the "balloons", for example.
That scene at the end where they are in the fishing grounds. Just the cries and screams of dismay as the crowds of fish try to swim away from the net. and then knowing that they are going to be hauled up and die of suffocation or worse. Imagine if you were one of the fish that wasn't in the net but someone you knew or loved was.
When the baleen whale was first seen. The way it appeared to be a little fish from a distance is...unsettling. Plus the way it just comes up from behind them and opens its mouth...
Made worse a scene later when it shows Marlin and Dory in the whale's mouth. Dory oblivious but Marlin perfectly aware that they are in a large predator's mouth, just moments away from being swallowed. His dejection and terror is palpable, especially with his realization that he let his son down.
Nemo's first attempt at blocking the tank's filter. The filter is sucking him back down the tube while his tank friends are desperately trying to reach him with a plant, the only thing stopping Nemo from becoming shredded to bits.
Imagine this: You're walking down the street in a bad neighborhood, and you see a young woman alone by the side of the road, pacing in circles around a lamppost. She's visibly distressed, so you go and ask her if she's okay, and she blurts "I don't know where I am." Then she tells you she has no idea what's going on, and the only thing she thinks she maybe knows is that she "lost somebody", but she can't remember. So it's not just that she's lost - she actually has no memory of getting there at all or what she was doing beforehand. How concerned would you be?
If Nemo hadn't found her by chance, how long would Dory have been swimming around that chain for?
Not to mention the possibility of her having a run-in with a nasty predator...
The trench that Marlin and Dory find before swimming up to where the jellyfish are. Not only does the trench itself look particularly haunting, but the low, creepy music that plays as they're both gazing into it is very unsettling.