My favorite films on this topic:
Social network - a film about Mark Zuckerberg, about how Facebook was created and what difficulties we had to go through.
Jobs: the empire of seduction - promotion Apple from scratch. It's more likely not about programming, but the very idea of technology. The film fills with motivation.
The swordfish password is also a very good film, although the main theme is not programming or even technology. One of my favorite. They say a lot about hacking in films, but personally I did not find strong blunders in this film, although whoever looks, may find it.
Halt and Catch Fire is an American drama series that tells about the events around the rapidly developing computer industry. Atmospheric work showing the role of innovation and innovation in the modern world and the lives of characters who are at the forefront of the development of the new computer industry.
Silicon Valley is a sitcom about a team of guys who made a revolution in the field of archiving. Vivid characters, superb greasy humor - all this will ideally go in the company of your friends shit coders in the evening under a bottle of beer.
Although the above is not exactly movies, but I think it will perfectly fit as an answer!
If the films are not documentary then ...
The Solial Network is a film about Mark Zuckenberg and the creation of Facebook.
Mr. Robot is about the computer genius Eliot and his psychological state. The destruction of the most sinister company Evil Corp (as Eliot is called).