Hackers is a classic. That is the one thing my girlfriend and I can agree on, we both love the movie and watch it together once a year or so.
I actually won a rather sweet backpack at a security conference last year for my geeky knowledge of all things from that film. I think it peeved off some people when I raised my hand every single time they asked a question related to that movie.
It was a game of questions regarding hacking movies. So they had a few from Matrix, Wargames, Firewall, Hackers, Sneakers, and a couple others. I dominated the Hackers movie questions though.
For the Matrix, they asked what the exploit was that Trinity used to gain root access. Was pretty fun.
Entertainment is my main requirement for a film to be 'great'. Probably why Army of Darkness is my all time favorite film. Cheezy... unrealistic.. but damn it's awesome.