The only prop that counts.
The Bird. The Black Bird, Sweetheart.
Pointedly NOT The One Ring.
Anduril on the other hand…
The spinner weapon from Krull
or maybe freddy’s knife glove from Nightmare on Elm Street
The Dude’s cardigan from “The Big Lebowski”.
Remember-it is only a prop and not the real thing.
I know, but as Tolkien did (he was really upset when a fan gifted him a giant replica of the Ring and ended up using it as an ashtray) I consider it an evil, obscene thing.
The sword Buckingham gifted to D’Artagnan in the “The Four Musketeers.”
Nautilus model from 20,000 Leagues Under The Sea.
Ben Hur’s chariot.
Well, now I kind of want to change my answer.
Am I allowed James Bond’s Aston Martin DB5?
Edit: If not, the Hoverboard from Back to the Future 2
The Millennium Falcon from the original Star Wars movie (not the big one they walk to but the model used for flying scenes).
(I would do Star Trek but I actually have that…or will very soon…waiting on delivery…replica)
The car is just a car, and the board doesn’t hover, but sure.
NO, it’s not just a car, it can shoot little rockets and rotate the licence plates. 
True but still…a freaking Aston Martin DB5 would be great to have even without the ejection seat and machine guns. (Although I imagine the insurance for that car would be painful)
So it has three expired British plates instead of just one!
Lots of things I’d like to have, but if I had to narrow it to one: Obi-Wan Kenobi’s lightsaber.
I was also considering a light saber…Luke or Vader’s. They would be great. (I also would like Mace Windu’s light saber…and Yoda’s while we are at it.) Any (including Obi-Wan’s) would be awesome to own.
Beat me to it.
No question: Robby the Robot from Forbidden Planet (and subsequent other movies).