The entire halloween episode "The Shinning" in Treehouse of Horror VI is based on the movie "The Shining" from 1980.
Wendy, Danny, Jack  
Overlook Hotel  
Jack Torrance and his family moves into the Overlook Hotel, as caretakers for the winter.   Mr Burns hires the Simpson family to take care of the lodge for the winter.
The elevator/lift opens and lots of blood flows out.   The elevator/lift opens and lots of blood flows out. Mr Burns says that that's odd, because the blood usually gets off at the second floor.
Danny, Wendy  
Wendy and Daniel takes a walk through the maze.   There's a maze at the lodge, but as opposed to Wendy and Danny, Bart walks straight through thanks to his hedge cutter.

Wendy, Danny, Dick

Dick (to the right) knows that the little boy's name is Danny (in the middle), because they both have telepathic powers.   Willie discovers that Bart got telepathic powers. But Willie calls it "Shinning" instead of "Shining" because he don't want to be sued. Wille says that if Homer goes crazy, Bart can contact him.
Jack, Bartender  
    Moe appear as a ghost, and says that Homer will get a beer if he kills his family.
Homer writes "NO TV AND NO BEER MAKES HOMER GO CRAZY" all over the walls, just like Jack writes that "All work and no play makes jack a dull boy" all over his papers.
Wendy, Jack
Jack has gone crazy, and Wendy threatens him with a bat. She eventually hits him.   Marge threatens Homer with a bat, just like Wendy in the movie, but Homer screams when he sees himself in the mirror and falls down the stairs.
Marge locks up Homer in the freezer, just like Wendy does. In the movie the ghosts opens the door for Jack so he can kill his family, but here they have to carry Homer out, because he just wants to eat.
"Here's Johnny!"  
Homer uses an axe to cut through the door just like Jack and screams "Here's Johnny!", before he realises that he has cut through the wrong door.
Homer cuts through the second door and screams "David Letterman". He sees Grampa Simpsons who says: "Hi David. I'm Grampa."

Homer cuts through the third door and says: "I'm Mike Wallace, I'm Morley Safer, and I'm Ed Bradley. All this and Andy Rooney tonight on 60 Minutes." The family runs away screaming.

Danny writes REDRUM on the door, which is Murder backwards.   In 9F12 Brother From the Same Planet, tries Bart to contact Homer with telepathy, and Milhouse ends up writting "trab pu kcip" on the wall which is "Pick up Bart" backwards.
In the episode 5F06 Reality Bites Marge became a real estate agent and sold the "Murder House" to the Flanders. Ned tells Marge that they're painting Todd's room with red painting. Todd says: “REDROOM, REDROOM (REDRUM) over there!”   Maggie playing with her blocks: RedRum = Murder backwards
Bart uses his "shining" to contact Willie. Just like Danny contacts Dick Hallorann
in the movie. Willie comes to help them but gets chopped in the back before he has done anything.
In the second story from the same Halloween special "Time and Punishment", Willie shows up in the Simpsons house to help Homer return to his own dimension, but Willie gets stabbed in the back, by Maggie, before he has done anything.
In the third story from the same Halloween special "Nightmare Cafeteria", Willie shows up to help the children escape from Principal Skinner and the rest of the teachers who wants to eat them. Willie gets stabbed in the back, by Skinner, before he has done anything.
Homer chases his family out into the nature, but Lisa finds a miniature tv and gives it to Homer so his urge to kill is fading.

Jack chases Wendy and Danny into the nature. He follows Danny into the maze, but freezes to death before he gets out. Danny manages to get out, and he and Wendy leaves in the snowplow Dick arrived with.

  The family ends up glaciated, just like Jack, and when they can't change away from the "Tony Awards" because they're all frozen, Homer's urge to kill starts rising again.

All the Simpsons images were captured by Henrik, except the "trab pu kcip" which is from Destination: Springfield. Most of the images from the movie were found on the following sites: