In "Devil Dog", Taz, in this version, is very monstrous and has a murderous rage. Oh god, the evil red eyes and the entire scene with him nearly eating Sylvester and Tweety, it can practically make one wet herself. Sylvester fleeing down that dark hallway with a look of sheer terror on his face (not played for laughs terror— REAL terror), might be the scariest part of that sequence.
Lola's stalker-centric song, "We are In Love" was just filled to the brim with Yandere undertones, and if that wasn't enough, at one point, there is a shot of her standing outside Bugs' house in the middle of a lightning storm, silhouetted, with an eerie Slasher Smile the only thing seen in between the lightning strikes.
Bugs:You're the reason I always keep my shades down!
The episode where Daffy thinks that Porky is a serial killer. It does have a rational explanation, but the leadup is genuinely unsettling.
"PUT DOWN THE STAPLER OR I'LL WRITE ALL OVER THE PIG'S FACE!!!!!"
Bugs becoming addicted to Spargle. It's a lot creepier than it sounds.
Especially since it actually looks like a drug addiction.
Well, Spargle is made from an illegal drug.
Yandere!Daffy from the first episode. Especially his unnervingly empty looking smile.
Daffy: I'm going to be the best best friend that any best friend has ever had! Muahahahahahaha!!!!
Potentially Fridge Horror, but Bugs' "What did you parents do to you?" may be more unnerving when you consider that, in "That's My Baby", Daffy says he doesn't remember anything before age 15. It's entirely possible that Daffy's parents are responsible for his behavior, beyond the domestic strife, and Daffy's totally unaware of it. Then again, Daffy's generally unaware of his own behavior, so maybe it evens out.
In "Itsy Bitsy Gopher", there is a Giant Spider that has a Very Bad Bite, It's appearance may be cartoony , but it has a very frightening appearance for spider haters. It doesn't help that Bugs almost had to have to have his hand amputated if it wasn't for his luck.
If the trans-dimensional scene in 2001: A Space Odyssey creeps you out, you might want to keep that in mind while watching the Coyote-Road Runner short "Unsafe at Any Speed". It is pretty heavily invoked.
All of Cecil Turtle's actions in "The Shell Game". First off, he pulls plenty of Nightmare Faces, even one that is pretty much the Grinch's "idea face". Later on, when Bugs and Porky uncover his scam, he actually attempts to murder them both to keep them quiet.