A movie can certainly be in more than ONE category, or can be very unusual for its category, but the above-mentioned films are still Sci-Fi

Matrix and Back to the Future DEFINITELY fit the definition, what with the time travel and AI. Sci-Fi simply covers a lot of ground.
My favorite on-screen Sci-Fi in NO particular order--favorite by a combination of enjoyment and overall quality (some have more of one than the other!):
Serenity/Firefly
The new Battlestar Galactica
City of Lost Children
Delicatessen
Being John Malkovich
Solaris (US remake--sorry!)
Close Encounters of the Third Kind
Doctor Who
Sky Captain and the World of Tomorrow
Alien/Aliens
Orlando
Blade Runner
Minority Report
A Scanner Darkly
Dune (books better than miniseries; Lynch movie fun its own weird way)
Fahrenheit 451
Dark City
Phase IV
28 Days Later
12 Monkeys
Brazil
I do appreciate Star Wars for its time--and I LOVED it as a kid--but it doesn't have the OVERALL qualities to put in among my very favorites in a lasting sense. It's great fun in some ways, average or poor in others (like depth of character development). Same for Star Trek--although I'm still a fan of TNG, cheesy though it seems these days. And I bet DS9 would have been a favorite, I just hardly saw any of it. Same for Babylon 5 maybe. I enjoy some humorous sci-fi like Galaxy Quest, but I can't rate it with my favorites. Similarly, I can appreciate some black and white classics, but can't call them favorites.