My first thought was the stair-car from Arrested Development, I’m either ashamed or proud to admit - I haven’t decided which.
There’s this scene in Robocop, in which it is revealed that the designers of the original model hadn’t considered stairs.
If I’m envious of such a recollection, then you should be prouder than Tobias after getting another treatment for his concerning hair loss.
Near the end of Straw Dogs Dustin Hoffman is pinned on the stairs but some dude’s foot before he (dude) is rifled down by Susan George.
Hah! Yes. I need a real keyboard back 
In Titanic, the iconic scene at the end where old Rose dies in her sleep and is back on the ship, where a young Jack waits for her at the top of the sweeping staircase.
I seem to recall a scene from Canadian Bacon that involved a whole lot of stairs (escaliers).
One of my favorite horror movies: The Changeling. Trish Van Devere goes up the stairs and you just know bad shit is gonna happen to her. When she gets to the third flight and says, “John? I don’t want to come up there”, a half dozen people in the audience shouted “THEN DON’T!”.
And sure enough, bad shit happened.
Nightmare on Elm Street gooey stairs scene
Psycho - The detective played by Martin Balsam slowly ascends the main staircase in the spooky old Bates mansion. It does not go well for him.
After trying to crush Talking Tina’s head in a vise grip and then trying to blow torch and then radial arm-saw her head off (all unsuccessfully) a flustered Telly Savalas, in a Twilight Zone episode, comes to his end by tripping over her strategically-placed self on the top stair, as he tumbles down the stairs to his death.
Nice post script when his wife happens upon the scene, and when she picks up the doll, it says, "My name’s Talking Tina…(then slowly opens its eyes)*…and you better be nice to me."
A very frightening scene on a spiral staircase in The Haunting (the original Robert Wise version). I was terrified of spiral staircases for years after seeing that movie.
What about the running joke that’s such an important part of the plot - crazy Uncle Teddy who thinks he’s Teddy Roosevelt and re-enacts the Rough Riders’ charge up San Juan Hill every time he goes up those stairs:
no stairs = no Teddy Roosevelt = no Happydale = no plot :DThere’s that scene in* Scarface*…
The play a pretty important role in The People Under The Stairs.
Too many horror films to mention - you know, creeping down some scary stairs into the basement… Best is probably the basement stairs from Evil Deads 1 and 2 where Ash climbs down slowly only to have his ankles grabbed by a demon hiding behind them…
If we can open this thread up to books with prominent use of stairs, then I submit House of Stairs, a surreal, mid-70s “teen” novel. It was one of those post-60s youth novels that were “relevant” and “spoke to the younger generation” and all those other 70s-era buzzwords.
Apparently, a movie version was in the works, but is in limbo currently.