The shot of Lemongrab in "Too Young" with his eyes rolled back into his head, with only the whites exposed.
There was a deleted scene from that same episode, where Lemongrab sends a tiny candy kid to the dungeon. When the kid meekly tries to protest, LG makes an exceedingly creepy, deranged face, and the kid leaves the room in tears.
We don't see the face Marceline's dad makes at the Ice King in "It Came From the Nightosphere", but judging by the Ice King's reaction it was pretty terrifying.
In the Animaniacs Goodfeathers cartoons, the usually placid Godpigeon can turn his face into a terrifying monster face◊ at will (making this qualify for Demon Head as well). He does it in two cartoons: to cure Squit's hiccups in "Hiccup," and in "Pigeon on the Roof" as Restrained Revenge on Pesto after the latter confesses to fantasizing about murdering him and taking over the flock. He also has has the same face in zombie form in Pesto's actual nightmare from the same cartoon (a parody of "Tevye's Dream" from Fiddler on the Roof with the Godpigeon in the Fruma Sarah role).
Calendar Girl in "Mean Seasons" hides her face behind a White Mask of Doom — her appearance is perfectly normal, even beautiful, but being cast aside by the modeling industry as "too old" warped her perception so that she sees only the minor flaws and thinks of herself as hideous.
In Ben 10: Omniverse, Toepick, is a being with a metal grate over his face. Whenever he lifts the grate (his face is never shown to the viewer), everybody (according to Word of God, even a Celestialsapien) is terrified beyond belief. Only beings who are blind or emotionless are immune. Apparently, even Toepick himself is not immune if he were to see his own reflection. Ma Vreedle is also immune. She's seen worse. Whether this is true for actual members of his species or just for Toepick (a.k.a. Ben) is unknown.
Cartoons That Never Made It: Frothy Dawg, the title character of one short, qualifies.. The sight of his foaming rabies-induced rictus grin is enough to scare a lot.
Centaurworld: In "Holes, Part 2", when Comfortable Doug suddenly shouts "tell it to the judge!", his goofy-looking rounded teeth suddenly become fangs, he loses his accent, and his voice gains a distorted, echoing effect.
When Numbuh 3 gets quite upset, her head will, in any way, shape or form, becomes demonic. Case in point: when she finds out her stuffed toys have been destroyed by monster lice and breaks down crying:
Numbuh 1: It's okay, Numbuh 3, we'll get you some new toys. Numbuh 3: Toys? I don't want toys. I WANT REVENGE!!!
Father's angry face in the season 1 finale, where it suddenly turns demonic and shows a mouth full of sharp teeth. This is the only time we see his mouth when he's wearing his shadow suit.
The Cuphead Show!: Baroness Bon Bob makes a terrifying maniacal fanged face from the episode "Sweet Tempation", after she turns Cuphead and Mugman into candy.
One Cutaway Gag parodied The Ring; Peter watches the cursed tape, despite fair warning, and in the next cut we see him with a Nightmare Face, just like what you might expect from a reference to The Ring (The joke is that the cursed video was a copy of Mannequin; Take That!).
The character of Death also apparently has one of these, causing Peter to scream in terror when he see it and vomit afterwards.
Snake Eyes is implied to have this by the unnerved reaction of several bikers who saw him unmasked. Scrap-Iron's scarring after taking a missile to the face definitely qualifies.
In the Marvel comics, Cobra Commander wore the mask just to stay anonymous, but in the Sunbow cartoon, the mask was to hide his face. Destro, himself masked but a normal guy underneath, is repulsed in one episode when walking in unexpectedly on Cobra Commander dining.
And in "Wishbones" when Pud'n finds the wishing skull he wishes for a cute little bunny to love, when he gets the bunny he picks it up and hugs it, it then headbutts him and roars at him making a hideous face in the process, for that moment the bunny has fangs, tusks, a forked tongue, and horns.
Alastor has an especially terrifying face with black sclera, glowing red irises, pupils like radio dials, and a fangedSlasher Smile while static and demonic sigils pop up around him. The Freeze-Frame Bonus glitch when he pulls this face shows an even more frightening one where his pupils disappear, his irises turn to glowing pinpoints and blood is oozing from his mouth. He's the current page image.
Charlie, during her musical number in the Pilot Episode, pulls a fanged Slasher Smile with red eyes and large devil horns bursting out of her head.
Comically averted with a creepy character called Teehee Hummy tums, who wears a burlap sack with a weird face drawn on it over his head (as does his family). When he takes it off at the end of the episode, it turns out that he's so stunningly beautiful that his face projects a halo of light (the viewers dont get to see it, but the other characters are all mesmerized and throw money at him as thanks for gracing them with his presence).
"Too Many Pinkie Pies" parodies this trope by having one of Pinkie Pie's clones turn her face into... G3 Pinkie's.
Pinkie Pie: Betcha can't make a face crazier than... THIS!
The Pluto the Pup cartoon "Pluto's Judgement Day" in which Pluto dreams he winds up in trial in Dog Hell, the cat prosecutor makes a rather terrifying face when he says "Justice!".
A particularly extreme one◊ happens in "Ren Seeks Help", where Ren's eyes become huge and bloodshot, and his lips flap back and away from his mouth to reveal gums studded with small, misaligned pointy teeth. Ren makes another terrifying face later in the episode, after he beats Mr. Horse.
The face Ren makes in "Stimpy's Pregnant", when he finds out Stimpy's "pregnant" and attempts to abort the "baby", is also pretty frightening.
One in the original Ren and Stimpy happens when Ren shouts, "AT LAST I HAVE CONTROL OF YOUR TV SET!", before immediately switching to a face that is much more pleasant to look at. His already protruding eyes are bulging so much that one would expect them to jump out any moment and his mouth is nothing less than utterly disgusting with a few misshapen teeth visible from his also exposed gums.
Charlotte in the spin-off series, All Grown Up! looks a bit unnerving thanks to what was clearly too much cosmetic surgery. She made Didi scream in terror at least once.
In "Brother from the Same Planet", Bart is so mad at Homer for being late to pick him up that he has a brief Imagine Spot of Homer's face burning and melting, with his face looking like a skeleton covered with blood and rotting skin, and his eyes devoid of pupils, while moaning "NOW HOW 'BOUT A HUG?".
"Treehouse of Horror V": In "The Shinning", while being manipulated by the ghostly Moe, Homer makes several terrifying faces; at one point, he mocks Marge for being afraid of them, he makes one and looks at his reflection in the mirror, and scares himself.
Part of the reason SpongeBob and Patrick mistake Sandy's pet caterpillar-now-turned-butterfly Wormy for a monster in one episode is because the Butterfly is supremely hideous to the point it probably gave more than a few kids actual nightmares, since we actually get to see its face up close multiple times throughout the episode, which is shown through actual footage of a horsefly with a loud buzzing sound.
In the Teen Titans (2003) episode "Crash", Raven scares Gizmo into helping to cure Cyborg by lowering her hood. We only see her shadow on the floor next to Gizmo, but there are implied to be tentacles coming out of there. Interestingly, prior to it Robin indicates that he wants her to do this. Which means he knew Raven was capable of making such a face.
Young Justice (2010) has a moment when Klarion the Witch Boy's face...shifts into something pointed and ratlike as his eyes go demonic. Many fans have cited it as one of the scariest parts in the whole series.