Biography
The human face is supremely important on a social and biological level. Most of our non-verbal communication comes from reading subtle facial movements, and its importance in our cognitive thinking is best shown in our tendency to see faces in inanimate objects (think of how many times you've looked at a rock face and thought you'd seen two eyes and a mouth). So there's something genuinely disturbing to most people about seeing a face visibly distorted, mutated, or rearranged ... so, naturally, this type of Body Horror is one of the most common Horror Tropes.
A Sister Trope and effective primary component of Nightmare Fuel.
It is in fact at least Older Than Feudalism — armies over the world have based their war masks around this trope, and in mythology and folklore, just about any self-respecting demon or supernatural evil will have one.
More recently, it has also become a staple of Surreal Horror.
This is a main symptom of Coming Back Wrong. Most humanoid examples of Our Monsters Are Weird will fit this trope.
This trope is commonly doubled with the Jump Scare in a Screamer Prank.
Sub-Tropes include:
Black Eyes of Crazy: A character is shown to be evil by having black sclera.
Black Eyes of Evil: Evil characters' eyes are completely black.
The Blank: No facial features at all.
Cheshire Cat Grin: An unusually wide, mischievous smile.
Cute Creature, Creepy Mouth: A cute creature has a horrifying mouth.
Eyeless Face: A face is devoid of eyes and eye sockets.
Facial Horror: The face is disturbing because of scarring.
Game Face: A character's face becomes frightening when they reveal their true self.
Ghostly Gape: The eyes and mouth are empty black pits.
Glasgow Grin: A large grin created by slicing the cheeks.
Glowing Eyelights of Undeath: Undead beings have glowing eyes.
More Teeth than the Osmond Family: A character's mouth is full of numerous sharp teeth.
Red Eyes, Take Warning: Red eyes indicate a character is evil or dangerous.
Scary Teeth: Character has a mouthful of sharp, predatory fangs or heavily rotten, disgusting teeth.
Slasher Smile: Character has an evil, bloodthirsty, frightening grin.
Two-Faced: One side of the character's face is disfigured, distorted, discolored, or otherwise different from the other side of the face.
Wide Eyes and Shrunken Irises: Beady irises generally indicate that a person is unhinged.
See also:
This trope's well-meaning (but still scary) sister, The Grotesque.
Game Face, which comes into play when a supernatural villain disguised as a human flashes his true form's Nightmare Face to scare someone.
Demon Head, cousin to this trope.
Demonic Head Shake, when the head shakes uncontrollably
Take Our Word for It, when the face is too grotesque to even show.
Interesting tidbit: this is one theory as to why some people are afraid of clowns. Exaggerated mouths, bulbous noses, and pin-prick eyes are downright terrifying to young children who haven't yet figured out that the person is just wearing make-up and not deformed.