The Hunchback of Notre-Dame: Hugo, representing Quasimodo, is living up in the attic.
Basket Case: Hugo wanting to be sewn back together.
The King and I: The segment title, "The Thing and I," is a parody of the film and play, The King and I.
Twilight Zone: "The Genesis Tub" is inspired by the 1962 Twilight Zone episode called "The Little People," where astronauts stumble upon a tiny civilization on an asteroid.
The Outer Limits: "The Genesis Tub" also closely resembles the two-part series premiere of the modern incarnation of "Outer Limits" titled "Sandkings" (parts I and II respectively) which first aired a year and a half prior to ToH VII. The main character "grows" his own mini-civilization which experiences rapid generational advances, and begins to build complex structures out of the sand. The main character becomes power-crazed with a "god complex."
Claw Game: The way Homer is abducted is reminiscent of the claw game (giant claw picking him up) and its difficulty (dropping him first time around).
Citizen Kane: The segment title, "Citizen Kang," is a parody of the 1941 film Citizen Kane.
Scooby Doo: When Homer unmasks the presidental-candidates Scooby Doo and his gang have the same reaction of Ripping off the masks of the villains.