This is based on opinion. Please don't list it on a work's trope example list.
Nightmare Fuel / The Muppet Show
The infamous Hugga Wugga skit, involving a Lyrical Dissonance from a stalked eyed creature singing "You are my Sunshine", the aforementioned creature who's violently abusive to anyone who doesn't sing the same lyrics as he does and the poor beaked sap that's abused by the former. It starts off creepy enough with the steam nose abuse, but takes a darker turn when the beaked monster starts singing the same song as the stalk eyed creature; and finally when the Hugga Wugga shoots off the stalk eyed creature's head he is legitimately confused and terrified when it continues to sing without a head
The whole Alice Cooper episode, especially "Welcome to My Nightmare"!
Vincent Price's version of "You've Got A Friend" starring the creepy muppet Uncle Deadly.
There was a skit featuring a gloomy guy in a room with skeleton singing about how happy he was. Mild nightmare fuel!
The Mummenschanz episode, especially the clay faces.
Miss Piggy's initially heart-wrenching rendition of "What Now My Love" gradually turns creepy and menacing. Just keep watching the chorus members as the number progresses. Good night.
The Zero Mostel episode has a sketch where Mostel recites a creepy poem about literally banishing his fears (as in making various creepy-looking Muppets gathering around him vanish into thin air). It ends with him coming to the unsettling realization that he might be the embodiment of someone else's fears, and that they will make him disappear... which is exactly what happens. It gets worse when you realize that Mostel died before his episode aired.
"You're Always Welcome at Our House" (sings Marisa Berenson with a demented smile....)
"I've Got You Under My Skin" is a musical skit featuring a rather unsettling looking creature called Behemoth (More recently called Gene) cheerfully seasoning and then devouring Shakey Sanchez.
It's somewhat mitigated by the episode showing Shakey backstage with Kermit after the number, in perfect physical health. On the other hand, he's terrified out of his mind and unable to speak clearly.
The episode in which Alan Arkin was the guest involved him accidentally drinking Bunson Honeydew's Ultra-Powerful Jekyll-and-Hyde potion. While a lot of it's Played for Laughs (his "transformation" involves him growing a unibrow and fangs and lurching around like Frankenstein's Monster) it's still pretty creepy, especially considering how unpredictable it is. And later, Kermit drinks the same potion and terrorizes a cute bunny that had just asked for his protection.