Gattaca and Brazil are among my favorites too.
I haven't seen Matrix in many years, it doesn't have anymore rewatching value for me personally.
If we have come to sci-fi discussion, I would recommend to everyone a really underrated one - Pandorum (2009), it is one of the coolest and shocking ones I have ever seen but like most lower budget movies it went under the radar.
Pandorum was a nice surprise, when I watched it years after release. Surprising also as I am not used to such good german movies.
And if you like Sci-Fi you have not too much big budget movies to choose from, as most producers see at as niche and don't allocate a lot of money.
Also, the list of SvennoJ is very comprehensive for great SF-movies to watch, but misses the original Ghost in the Shell.