This is a hard choice, I've got a degree in media so narrowing down to just three films is difficult.
These are not my favourite films, but they are ones everyone should see:
12 Angry Men
Good Morning, Vietnam (It was this or Full Metal Jacket; which suffers with the second half).
The Trueman Show (just because I studied Post-Modernism,).
My favourtie films are
Patlabor
Batteries Not Included
Unbreakable (& The Brave One, I always put the two together for the way they reinvent the vigilante/hero genre)
Groundhog Day