Lots of choices, but "The Great Escape" is one of my favorite movies of all time, and the ingenuity used to overcome adversity in a POW camp helps make it great. "The Right Stuff" about the Mercury program is also powerful, and the book is much more insightful about the conflict between the test pilots like Yeager and Crossfield and the more highly publicized astronauts. "Apollo 13" - the geeks win! "Castaway" "Swiss Family Robinson" and "Robinson Crusoe on Mars" have a similar theme of using ingenuity in a shipwreck situation. "Bridge on the River Kwai" and "October Sky" are both excellent, as well, portraying perseverance in the face of defeat. Having worked in automotive industry, "Tucker: The Man and His Dream" is a great film, although bittersweet on many levels, familiar to most engineers.
On a humorous note, "Real Genius", "Best Defense", and "Short Circuit" top my list for engineering comedies.
I don't know about the movies, but if you only ever see one play, make sure it is "Copenhagen" by Michael Frayn. It is a brilliant investigation of the meeting between Bohr and Heisenberg during WWII as seen through the lens of the uncertainty principle. (Not directly engineering but something all engineers will have covered during their education.)
A great movie about smart college kids having fun with science/engineering. It presented science/engineering as cool and fun. Which, of course, it is! It was largely responsible for motivating me to go back to school to get my Bachelors degree...
Like PureGenius I also recommend Brainstorm. The prototype "hat" is HUGE with nitrogen pumped cooling. Then they have a breakthru in size when they perfect an ASIC and can shrink it down to the size of a headband. A revolutionary concept for a 1983 movie.
"Bridge over the River Kwai" is a great movie, made even better by the very good protrayal of the British approach to civil engineering under adverse conditions. Schedule constraints play a big role, just as they do in most real life engineering projects. Perhaps most importantly the single-mindedness of the Colonel in getting the bridge built on time while ignoring the bigger picture of winning the war is typical of the short sighted vision of many engineering managers.
I also liked "The Rocketeer" as it was not too much a stretch of reality, after all, rocket packs are real, and it did show the problems in development and using a prototype before it is ready for prime time. The inclusion of a Zepplin and the Griffith Observatory are science/engineering bonuses.
I like Independance Day, where an engineer creates a virus to defeat an alien army, then learns how to fly one of their ships, travels to the mother ship, connects and logs in to their newtork installs the virus and brings the whole alien army down.
I'd like to mention Brainstorm with Christopher Walken. It takes a device capable of recording the mind from prototype to production. It also looks at one of the great mysteries of life when a death is recorded so it can be experienced by the living. Even though technically it's pushing it a little this movie makes you really want this technology to be real.
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