deemed to be the most significant in the history of film. Note that "most significant" does not mean "best" or "most popular" or even "most influential." Some of the films may be all three of these, but not all of them are -- indeed, some films in The Canon aren't objectively very good, weren't blockbusters and may not have influenced other filmmakers to any significant degree. Be that as it may, I think they matter -- in one way or another, they are uniquely representative of some aspect of the science fiction film experience.
Here is the list. I have bolded those movies I have seen.
The Adventures of Buckaroo Banzai Across the 8th Dimension!
Back to the Future
Bride of Frankenstein
Brother From Another Planet
A Clockwork Orange
Close Encounters of the Third Kind
The Day The Earth Stood Still
Escape From New York
ET: The Extraterrestrial
Flash Gordon: Space Soldiers (serial)
The Fly (1985 version)
Ghost in the Shell
Invasion of the Body Snatchers (1956 version)
Mad Max 2/The Road Warrior
On the Beach
Planet of the Apes (1968 version)
Solaris (1972 version)
Star Trek II: The Wrath of Khan
Star Wars Episode IV: A New Hope
Star Wars Episode V: The Empire Strikes Back
The Stepford Wives
Terminator 2: Judgement Day
The Thing From Another World
Things to Come
28 Days Later
20,000 Leagues Under the Sea
2001: A Space Odyssey
La Voyage Dans la Lune
War of the Worlds (1953 version)
This isn't too bad, with a nice mix of old and new movies. I am ashamed that I haven't seen Solaris, Metropolis, or all of Invasion of the Body Snatchers (I've seen excerpts). I haven't seen much anime, thus no Ghost in the Shell or Akira. I've seen many serials from the 50's, but I don't think I saw that particular Flash Gordon storyline.