Sharing your favorite movie with friends is a tricky balancing act. You want them to understand what they're missing, but you don't want to push them away from it.
That's why we have the internet. To do our jobs for us and share the best movies people need to see before they die.
Seven Samurai - directed by Akira Kurosawa
Akira Kurosawa is a Grand Master of cinema. The great directors of today are often imitating Kurosawa's work whether they know it or not...
As for the film itself, it's about recruiting 7 samurai to defend a town from a large force of raiders. It's 3.5 hours long and uses every minute to build the story organically. For example, it doesn't tell you someone is a great swordsman; it shows that swordsman winning a dual handedly. By the time you get to the film's climactic scenes, you know and care about all the characters and that makes all the difference in the world.
Not exactly a movie geek, but Dr. Strangelove is a timeless classic that will always be relevant and it's a masterpiece.
12 Angry Men. It's been decades since it came out and it still holds up.
The concepts in the movie (recognizing prejudice, etc) are relevant to every era.