In no order...
Children of Men - just blew my fucking mind, incredibly intense and beautiful and HUMAN
Sunshine - also very human, my favorite remotely recent sci-fi movie, enthralling and atmospheric and also psychologically terrifying
Saving Private Ryan - nothing really needs to be said here
Vozvrashcheniye (The Return) - incredible Russian film about a father returning to his home after being absent for the entire lives of his two young sons... wonderful cinematography and composition and the emotional tension is thick enough to choke on
Zero Day - the psychology and motives of school shooters fascinate me, and I have a kind of morbid obsession with Columbine in particular. This movie is a relatively accurate, faithful recreation of the Columbine massacre, down to the appearances and psychology of the killers, as well as relatively factual creative recreation of the events preceding and during the shooting. It's incredibly hard to watch and will absolutely disturb you, but I think it's important to examine and vicariously experience these things for the benefit of understanding our society and the monstrous acts it can drive individuals to commit.
Kontroll - beautiful symbolist Hungarian film, hard to describe but definitely worth a watch, has a kind of allegorical / fairy tale quality to it, and an amazing soundtrack
Blade Runner - another perennial favorite that doesn't need explanation... atmosphere, atmosphere, atmosphere
The Big Lebowski - the Dude abides
Eternal Sunshine of the Spotless Mind / Garden State - mandatory starry-eyed INFPness
all the old Indiana Jones movies
all the old Star Wars movies
Into the Wild