This Invader Zim page is full of spoilers. If you fear spoilers, walk away now.
Pretty much the entire show, really. It's odd to think that the only real difference between this universe and the Warhammer 40,000 universe is that in this one, Earth isn't strong enough to repel an invasion.
The infamous scene in "Bestest Friend" in which Keef has his eyes plucked out by robotic arms. Even if it is all shown in silhouette, via a shadow cast on a nearby building.
"Bad, Bad Rubber Piggy," which features Zim crippling and then murdering Dib as a child over the course of years, doubles as both Nightmare Fuel and Tearjerker worthy. Zim's response is to calmly walk away, drinking a soda.
Zim throws rubber pigs into Dib's past, replacing seemingly random objects in ways that cause Dib to have horrible accidents, progressively crippling Dib and making him more grotesque in the present, until he almost dies in the past and his father builds a super-powered robot body to protect him.
It's not really the worst behavior Zim's ever demonstrated, but the rapt, gleefully anticipatory look on his face as he watches the life go out of Dib's eyes — with accompanying flatline beep — is creepy on a personal level that he doesn't often reach.
Seeing a horribly scarred Dib (coupled with Hellish Pupils) in that robotic suit coming to horribly kill Zim. Is there any part of that that isn't scary?
At the end of that episode, Zim sends the final piggy into the past, only for it to replace his past self's BRAIN.
In the Halloween episode, that surprise screamer shot of that hideous monster with those big eyes during Dib's 'crazy house' bus ride? Not to mention that everything in Nightmare World is actually just a spawn of Dib's imagination. Nightmare Membrane and Nightmare Gaz are the worst of the bunch; Nightmare Membrane, while kinda cool looking, has a terrifying moment of capturing his son while his goggle eyes pop out of his skull, and his hands are replaced with metal claws. And then there's Nightmare Gaz, who's hunched over, skeletal, has More Teeth than the Osmond Family, but no bottom jaw.
Pretty much everything in that episode, really. To the point that Jhonen has said that he has no idea how any of this managed to get on the air.
Doubles as Fridge Logic when you remember that he was constantly butting heads with the Nickelodeon executives over many original ideas that censors hadn't allowed.
"Dark Harvest." It isn't that he steals people's organs. It's that he replaces them. Here's the list: a liver replaced with a hall pass that Miss Bitters has already specified will explode if the student leaves campus. A brain replaced with a can of soda so the poor receptionist can only foam at the mouth. Kids in the cafeteria have objects in place of their other organs. Gaz's beloved game is implanted into her side (she's still playing it). And Dib? You just have to see the end of the episode to how he turns out. Just check the whole nightmarish thing out here.
Zim them literally stuffs his own body with the stolen organs. Complete with a few of them spilling out. And instead of implanting the organs or anything like that...Zim eats them.
"Yes, you're a very healthy child! And such plentiful organs!"
The sudden surprise shot of Zim's organs with the X-ray and Dibs Organ-vision, complete with Scare Chord.
In a dark room, after Dib leaves, it gives the room a 'window shutter opening' light effect, twice in a row. The first time, the huge bloated Zim sits there smiling, and half a second later, he's gone.
Dib's drawing of Zim being dissected. If that weren't bad enough, Zim's fully conscious and his organs are pooling out of his body and onto the floor. Complete with what looks like blood!
Dib decides to stick to a boy named Torque Smacky who hasn't lost any organs yet to prevent Zim from stealing a pair of lungs. They enter a dark room where Dib turns around for one second & Torque disappears. We hear something drop & we see one of the dumbbells he was holding roll out from a corner. Cut to Dib yelling out the kid's name.
The moment in "Backseat Drivers" at the end when the brain parasite escapes and eats Zim's brain. It's even more terrifying when coupled with the fact that Zim explicitly stated that the parasite was capable of causing pain unlike any other form of known pain. Sweet dreams kids!
"Bolognius Maximus," where Zim and Dib slowly turned into bologna. Especially the scene in which the bologna is slowly mixed with Zim's skin. And the part where their bodies look swollen.
It can be a little unnerving to see the normally energetic GIR lifeless and blank-eyed after his brain gets transferred into the computer in "Invasion of the Idiot Dog Brain."
In "Walk For Your Lives", there's one instance where ZIM is talking to GIR, and the robot pulls something out of his head resembling A DEAD PUPPY, and shouts: "LOOK WHAT I FOUND! IT SMELLS REEEAL BAD!" and proceeds to wave it around manically, the puppy's eyes look lifeless... What the FUCK.
Judging by the barking noises, the puppy probably isn't dead.
NICK. Sweet jumpin jelly bean, Nick. He was intended to be a humorous Take That to Nickelodeon Studios, but he's just pure nightmare fuel. ZIM kidnapped the poor kid and performed experiments on his brain, and shoved a large, screw-like probe into Nick's head, forcing him to be happy all of the time. The kid has a perpetual, grimacing smile, but the look in his eyes is one of pure terror and pain.
Plague of Babies. A bunch of babies are shot into space, presumably to die. Aliens that LOOK like babies have their intelligence forcibly reduced to that of an infant, and they presumably live out the rest of their lives with the intelligence of babies.
All this and NO ONE mentioned the video from Door To Door. Hell, the whole POINT of the video was even to scare humans into buying Zim's candy! When you consider the ruined city, giant blobby monster who eats children's dollies, spider-cat, capture of humans, and Zim LICKING THE SCREEN WITH HIS ALIEN TONGUE...it did a damn good job.
Even worse, was that on the episode's debut (though the scene has been removed from all broadcasts and DVD releases since), the Statue of Liberty could be seen destroyed, only months after 9/11.
And let's not forget the scene from The Most Horrible Xmas Ever. Many people don't notice this, but when Zim is extracting the Santa knowledge from that mall Santa and he starts laughing, in the background you can hear what vaguely sounds like a chainsaw as well as the man screaming.
In the episode "Vindicated!", Dib goes to the new counselor Mr. Dwicky and asks what happened to the old counselor. Dwicky crouches behind his desk and says "Something... HORRIBLE!" Par the course for Zim humor so far, but then we pan up to the air vent right above his desk, and a raspy voice says "help... me!", complete with a POV shot from inside the grate! It's so freaky, it wouldn't be out of place in a horror movie.
Bloody GIR. A sneaky Take That to Nickelodeon. Invader Zim was denied the right to feature GIR covered in blood at some point in the series, and the concept was mostly scrapped, save for one piece of concept art. That concept art is subtly hidden, half-transparent in the single frames of the show. The art itself shows GIR covered in blood. That in itself might not be so bad if not for GIR being in his combat-mode and if he wasn't giving a Thousand-Yard Stare to the viewer.
Sometimes, the Malfunctioning Robot Parents are hilarious (Diarrhea, indeed). Other times, Zim has had to stop them from torturing a little kid so that they wouldn't blow his cover ("Come on over everyone, and help us EAT this little boy!"), and the dad's response is to give one of the most disjointed, disturbing versions of the "We don't spend enough quality time together" speech ever. And then they chase Zim through his own base, until he can bar them with a force-field. Even his computer calls them horrifying.
The ending of "Career Day" has to top the cake. Earlier in the episode, Zim begins to break out in a rash due to something slowly approaching called the Galactic Equinox, which causes all aliens off of their home planets to go into a hideous molt. While Zim is working at a fast food restaurant, his skin gets progressively worse, and once the planets and stars align for the Galactic Equinox, Zim's body BURSTS OUTWARD and fills the capacity of the restaurant, squishing its customers as they cry out for help, not unlike Tetsuo. During this entire moment Zim can be heard making a weird gurgling noise and his molting body is heard PULSATING as it grows to the point where it manages to squeeze and drip out of every opening in the building. Granted, it only lasts for about a minute and he instantly reverts to normal once it ends, but still...