There are plenty of scary episodes, but "Freaky Fred" stands out. He's obviously not right in the head, and he has sharp pointy objects within reach.
What makes Fred stand out from all the other villains of Courage was that he had no malicious or murderous intent with any of his actions. He was just an insane man with an almost fetish-level obsession with shaving people against their will (incidentally, shaving IS a sexual fetish). Despite his urges ruining his only relationship, his career, and his life in general, he shows no remorse for what he's done. And the worst part is that he's probably the only Courage villain to "win", in that he succeeds in shaving Courage bare, save for his tail (because that would be weird).
When he begins shaving Courage, 6-year-old children can be heard singing. *shudder*
The scene in the episode "Courage the Fly" where Eustace is chasing Courage as a fly. At one point, he gets Muriel's face stuck with fly paper and physically tears it off.
"Retuuuuurn the slaaaab...or suuuffer my cuuuuurse...", or King Ramses from "King Ramses' Curse". To some, it's not even so much the voice, or his equally creepy Leitmotif, but the way he moves. The way they animated him makes him looks just like an Uncanny Valley reanimated corpse. And he just stood out in front of their house the whole time, never moving from that spot, but always watching them.
In the beginning of "King Ramses' Curse", a giant black swarm chases the thieves who stole the slab. They bury it just in time for the cloud of doom to reach them. The camera pans to the side as they scream, and when it pans back, there's nothing left of the thieves or their car.
It's even better when you see it in motion. There are two reasons behind its "being creepier in motion": the vaguely off-key (or distorted, take your pick) background music, and the way the creature's eyes seem to imply that it is somewhat of an incomplete experiment, waiting for someone to put it out of its misery.
The Perfectionist, not only does she torment Courage and give him nightmares like the aforementioned dream, but when Courage finally accepts him for who he his she melts.
There's also a nightmare factory of an episode that is "Courage in the Big Stinkin' City". The whole episode is creepy, but it really cranks it Up to Eleven when Courage enters the house to retrieve a package. He opens a few doors that have cartoonish things in them (like an oncoming shark, or King Ghidorah), but when he opens the third door, he sees a girl (possibly 12 years old) playing the violin. She soon turns around revealing a freaky demon face and screams! And the camera is zoomed really close.
The Fridge Horror that is the monster behind the door from the same episode. Complete with skeletons around the room and a "help me" message written on the window. Even worse,we never find out what the monster is. Also, the whole entire reason Schwick sent Courage to get the package with a squeegee inside was only because he needed to remove the "help me" message. Possibly to lure more victims without suspicion.
The voice was surprisingly deep and ominous as well, but the real thing that made this terrifying was that this was an eerily-out-of-place live-action black-and-white disembodied head, interacting onscreen with Courage and his owners. The fact that they were shown onscreen at the same time just seemed to add to the guy being convincingly scary, and the different styles were even more dissonant than the Uncanny Valley-CGI Ramses, who never shared the screen with any other characters.
Any episode featuring Katz. Katz has no qualms about killing Courage or anyone, and he seems to have no traces of comedy whatsoever. His Leitmotif might be as equally creepy accompanying his appearances.
"A Night at the Katz Motel" is arguably his worst appearance, as his monstrous schemes at its worst take place in the middle of the night in a rundown motel. This episode is definitely not for arachnophobes.
He's a Serial Killer and most of his episodes imply the family are only the first in a long line of victims to fall into his traps...and the only ones to leave.
The zombie director episode "Everyone Wants To Direct". This episode had a dark atmosphere with barely any humor, and the plot involving killing someone in a movie for real is all too real. Also, said zombies turned out to be past serial killers who managed to slay a dozen people on a kid's show.
Some of Courage's screams can be very terrifying for kids, especially when some body parts are deformed or organs come outside. Watch it, if you dare. By far the scariest is the scream from "Car Broke, Phone Yes".
"Cabaret Courage". Getting dropped into a room which looks like (is?) the inside of a body, talking to a guy that looks like an ulcer, performing for that guy, getting dropped into some kind of digestive acid...
"The Mask", which features a girl in a flowing white dress wearing a giant creepy doll mask (and a terrible, raspy voice) who beats the shit out of Courage due to a hatred of dogs and spies on them to look for any sign of hypocrisy. The back story about her friend's abuse by a pack of dogs is a (not even thinly) veiled depiction of domestic abuse and forced prostitution. Courage The Cowardly Dog, a children's cartoon series with an episode revolving around an inner-city gangland drama.
"Curtain of Cruelty". When they wanted Murial to hit the hamster was bad, but when the hamster hit Eustace was worse.
Eustace being consumed by foot fungus in "The Clutching Foot".
It's Doc Gerbils World, It's Doc Gerbils World.
The Great Fusili. Specifically the ending. In It, Courage fails to stop Muriel and Eustace from being turned into puppets. Well, thanks God that this show has a Negative Continuity. However, this was originally going to be the last episode... There's also the nonexistent crowd, Fusili being turned into a puppet as well and the countless victims beforehand
Courage reenacts his usual situation with them, implying that he had gone through some serious Sanity Slippage by the episodes' end.
The Evil Vet from the episode "Remembrance of Courage Past". At least Katz in some episodes, had reason to try commit atrocities, but the vet just seems to enjoy being evil. He's the one who directly traumatized Courage as a child.
The episode 'Bad Hair Day' has a sequence where Courage goes into a building that farms humans for hair, and he sees dozens of humans hanging from rope on the ceiling... Most of whom have their eyes closed and are not moving.