I, too, am a fan of Sci-Fi/Horror movies, but not slasher movies. I got hooked back in 1961 when there were flying saucer movies and movies about mutations caused by nuclear testing. I've seen soooooooo many, the titles are swimming around in my head. You've gotten some good suggestions already. I will add my $0.02 worth:
The Day the Earth Stood Still
Them!
Tarantula
Earth versus the Flying Saucers (I think this is the title - the one with the "sand" - and that's all I'm going to say!
)
Tron (with Jeff Bridges)
Invasion of the Body Snatchers (the original version, 1950s, I think)
Red Planet (with Val Kilmer)
Dr. Jekyll & Mr. Hyde (with Spencer Davis)
Contact (with Jodie Foster)
Frankenstein (the original version)
King Kong (the original version)
Jurassic Park I
Stepford Wives (the original version)
Altered States (with William Hurt)
X-Men
Flatliners (with Kevin Bacon & Kiefer Sutherland)
Soylent Green (with Charlton Heston)
Dune (both the original and the newer version)
Outland (with Sean Connery)
Abyss (I think. I can see the movie in my head, but I don't want to describe it because I don't want to ruin it for you).
Twilight Zone series, Outer Limits series, FarScape series (I think that was the name - the series with Scorpius and the actress Claudia Black)
The Picture of Dorian Gray - not sci-fi, but thought provoking in terms of "what if there was an apparatus that showed our true selves."
The Haunting (the original version w/Julie Harris). Admittedly, again, not Sci-Fi, but
exquisitely done, such to produce chills and the thought, "Thank God this ain't a true story."
)
Hope this helps!