The way it inexplicably draws in anyone who gets too close to it. There are no words to describe it, as demonstrated in the first chapter. Atreyu can't even look at it without his mind rebelling at the non-sight. It is, quite simply, something that can not exist, because it doesn't.
The Sphinx Gate
G'mork. Apparently there's a good reason werewolves and vampires seem to have an innate hatred each other; for if they were to ever marry...Well, there you go.
Ygramul the Many, a myriad of blue beetles acting as one, most of the time forming a big spider but changing into multiple forms when fighting with its prey, or into a huge face with antennae instead of a tongue when talking to Atreyu.
Our hero Bastian's descent into becoming a tyrannical nutcase toward the end of the book.
The City of Old Emperors. While a city of nonsense may sound funny, it's not. Former humans are trapped in Fantasia with no memories of who they are, or what they are, engaging in endless, nonsensical tasks over and over forever. Truly a World Gone Mad.
The insane shlamoof creatures have quite the Monster Clown vibe going on. And towards the end it is revealed they have been pursuing Bastian for quite a while.
Uyulala's death and the songs she sings while she knows she is about to die are both this and Tear Jerker.
Yor's Minroud is an in-universe example. It's a mine where dreams are found, isolated in a landscape of eternal winter (particularly cruel considering the previous chapter was set in an area of perpetual summer) and tended by a single blind miner. The thought of having to work there, in the dark, is enough to make Bastian, who still has all the gifts of Fantastica including fearlessness, shiver in dread.
G'mork. His film incarnation has given many viewers nightmares. The first-person shots from his perspective as he hunts Atreyu are absolutely terrifying. And that's without getting into his personality. The film also removes anything sympathetic about his motives: "People who have no hope are easy to control, and whoever has the control has the power."
When he reveals his identity, G'mork looks extremely shocked for a moment... then it's replaced by a look of cold rage.
Falkor and Atreyu flying through the empty void after the Nothing destroys everything. The scene just feels so empty and foreboding with the music only adding to the feeling. Also doubles as a Tear Jerker.
The part where Artax sinks in the Swamps of Sadness. Tear Jerker, yes, but also prime Nightmare Fuel. If I heard right, if you let the sadness get to you, you sink! What this means is the swamp possibly subjects you to unbearably depressing images until you get sadder and sadder and sink!
The kid actor also apparently got scarred for life because he got hurt several times during filming - during his horse riding training, he fell off and got stepped on. Then evidently, his leg got caught in the elevator and he got pulled under.
Morla, the giant sneezing turtle, has robbed many a child of sleep on her terrifying appearance alone. Her -pardon me,- their cynical views, complete indifference to everything and possible schizophrenia do not help the situation.
Bastion screaming at her introduction didn't help.
The scene where the knight's helmet blows open to reveal his charred skull creeped many out for years.
Engywook: Fancy armor doesn't help. The sphinxes can see straight into your heart.
And right after this, when Atreyu's determination cracks and turns to fear and doubt, the Sphinxes' eyes slowly start to open...
That hideous anthropomorphic chicken thing from the second film.
The fact that there is actual Rule 34 of it only makes it worse.
A meta-example. Given the rumors about various injuries and traumas suffered by Noah (Atryu's actor) and the apparent death of (possibly several) horses, the sets, many of which already look rather dangerous, didn't seem to have any safety regulations.
Right before we cut back to Bastian, we see solid ground getting blown by the Nothing.
The Southern Oracle beginning to fall apart.
If you want to save our world, you must hurry! We don't know how much longer we can withstand the Nothing!
The implication that all the terrible destruction in Fantasia is deliberate and planned by a malicious being who is never seen or described.