It's not exactly a sophisticated effort (using a wardialer and guessing a backdoor password), but it's far better and more realistic than the majority of movie-style "hacking" scenes.
Sneakers, by contrast, has some interesting depictions of social engineering, as well as the amusingly low-tech yet effective approach of "point a camera at someone's hands while they type a password" (which remains a realistic danger today).
Hackers is dripping in 80s cheese, but that was what made it fun. And it captures how people thought hacking worked and what kinds of things people thought it could do: type something into a computer and take over a city's streetlights.
WarGames was another case of life imitating art imitating life, when the over-the-top NORAD command center set (the director called it "NORAD's wet dream of itself") became the blueprint for command centers everywhere going nuts with monitors.
A NORAD commander is quoted there: "A few years later, I was an executive officer with the Air Force Space Command stationed at Norad near Cheyenne Mountain. And I'm wondering, 'Gee, where can we get such cool-looking displays?' It was a good forcing function. It required us to all of a sudden say, 'If it really can look like this, why doesn't it?'"
Hackers is dripping in 80s cheese
In Ex Machina the main character appears writes a field sieve in Python to break some crypto. The code doesn't actually do that but it's still decent.
A bunch of older movies featured nmap.
Tron http://www.imdb.com/title/tt0084827/
The Net http://www.imdb.com/title/tt0113957/
Firewall http://www.imdb.com/title/tt0408345/
Blackhat http://www.imdb.com/title/tt2717822/
Who Am I http://www.imdb.com/title/tt3042408/
The Net always came across to me as a movie made by people who had never touched a computer. Without knowing what to write about (and after exhausting as many technical inaccuracies as possible) it just turns into a run of the mill thriller. It's kind of painful to watch. Hackers tosses out some jargon, but lots of the actual computer interaction stuff is completely obfuscated and contained in the fantasy of the world itself.
Can't say I've seen the rest, but I've added them to my list!
WarGames really nails the solo bedroom hacker of the 80s but then mixes in the DoD and general purpose AI to turn it into a coldwar thriller.
Sneakers is a clever, quirky, thoughtful adult hacking film.
Hackers though, teenage me ate up the feeling of the hacking culture that it espoused. When I read cyperpunk books, I pictured the environment and characters as places and people who could have come from this world. The sort of irreverent, authority denouncing, cybervandalism spoke to me. The Warez, Demoscen, ANSI art scenes all seemed to sort of be a kind of foundation that created a universe that this movie made manifest.
When this movie came out, I was still telneting, BBSing and gophering around "cyberspace". As soon as I found a writeable folder on an ftp server I'd make hidden folders and upload crap and tell all my friends. We'd stay up late wardialing and playing this soundtrack. We'd telnet to random IP addresses and then get excited when we'd hit a VAX system, just like in the movie.
It formed a kind of social scaffolding my nerd friends and I hung our digital world off of.
It's kind of laughable in many ways now, like many teen counter culture movement. But it still holds a special place in my heart.