Please don't list this on a work's page as a trope. Examples can go on the work's YMMV tab.
Nightmare Fuel: Looney Tunes
The Looney Tunes short "Now Hear This" is a No Dialogue Episode set in a surreal landscape that's apparently a minimalist version of London. It involves a British gentleman getting into all manner of at-times-creepy weirdness upon finding an apparently cursed ear trumpet. Strangely behaved shapes appear inexplicably, accompanied by discordant noises, and at one point the poor bloke is plunged into darkness while being menaced by dozens of mean, staring eyes and floating text reading "PUNK" and "WISE GUY". After abandoning the device in favor of his old one, we promptly find it was Satan's horn.
Worse if you look at the story as an analogy for an old man's struggle against the onset of dementia.
Rudy Larriva's Road Runner cartoons in general can be ominous and nightmarish at times (if you can get past the fact that they look like a cheap imitation of Chuck Jones' work), and not just the one above. Some good examples include "Highway Runnery," "Chaser on the Rocks" and "Shot and Bothered."
The Case of the Stuttering Pig.
Satan's Waitin', in which Sylvester literally goes to hell just for doing what cats do, e.g. chasing Tweety Bird.
"The Big Snooze" being the most blatant. Lampshaded in three Chuck Jones-directed cartoons: "Scaredy Cat," "Claws For Alarm," and "Jumpin' Jupiter", where Porky takes Sylvester to these scary places to sleep for the night, and only Sylvester can see the scary things just about to happen to Porky...
Porky In Egypt (1938): In this scene, Porky's camel Humpty Bumpty starts to hallucinate while in the desert heat.
Invasion of the Bunny Snatchers, while being one a modern-day favorite, never fails to give viewers the creeps. Especially the doppelgangers. *Shudder*...
A scene from "Greedy for Tweety", in which Sylvester is given sleeping pills and as he opens his eyes as he goes to sleep, the bulldog is coming closer and closer wielding a baseball bat, and Sylvester not being able to move or react because he's doped up on pills. The final shot has him raising the bat and POW.
The cartoon "Pigs Is Pigs", where a gluttonous pig is force fed until he explodes. Luckily, it was All Just a Dream.
The end of "Leghorn Swoggled", where Foghorn Leghorn is knocked unconscious (to the sound of a sputtering engine!) and dragged on a toy train into (presumably) Henery Hawk's oven. Made all the more scary when you consider that this is otherwise one of Foggy's less obnoxious cartoons.
The end of "Long Haired Hare", where Giovanni crawls out of the remains of the Hollywood Bowl, his tuxedo shredded, his face badly beaten, and his hair a completely different color. Bugs notices one last piece of the Bowl dangling from a support beam, cues the singer to sing that high note one last time, and then the last piece drops. Off camera, we hear a crash, and the singer goes completely silent...
The obscure Porky Pig short "Fish Tales" (1936, Jack King) is pretty unsettling when you're a kid. For those who haven't seen it, it involves fisherman Porky having a dream about getting caught by a family of talking fish who try to cook him alive in an oven.
Things are often disturbing for no other reason than how bizarre they are. Take the early Egghead cartoon where the hunter says that there are no other hunters about, whereupon a hunter emerges from behind every bush around him.
The Ducksters. "You'll be sorry!" So Daffy kills whoever said it with a rifle and proceeds with the episode.
The ending of Dr. Devil and Mr. Hare was the most disturbing for any Bugs Bunny cartoon as his Frankenstein's Monster he created to beat up the Tazmanian Devil then turns on him as Bugs wails with genuine terror, "No, no, no, not me, Frankie! Not me, Frankie! No, Frankie, No! No!" It's even more disturbing in that this was the final Bugs Bunny short of the Merrie Melodies series.
Actually, it wasn't. There was at least one more after that. Still very creepy, though.
Sylvester's insomnia and ensuing nervous breakdown in Birds Anonymous.