One example of something I like is "the mist"
Most Helpful Guy
The mist is a good movie but it's not really science fiction. The novel to the book is by Stephen King and Stephen King writes thrillers. I'd call this movie a thriller with some phantasy elements.
Probably my favorite science fiction movie is "Children of Men". It's quite socio-critical and doesn't just show you a boring recurrence of shooting and action scenes likes some of the movies that have been named here.
A big classic is of course "1984" but here I recommend you to first read the novel by George Orwell.
I also like "Gattaca", "Equilibrium", "Ex Machina" and "Her". They're all pretty thought-provoking films. "The Fifth Element" isn't a deep movie but it offers good entertainment.2