A TV show you think absolutely everyone should watch at some point in their life. You can make it a movie if you can't pick one show :)
Battlestar Galactica, no contest.
There are quite a handful shows out there that I think everyone should watch, but Battlestar Galactica is the one that tops the list. Even if you don't consider yourself a fan of science fiction or don't normally venture into this particular genre, I definitely think you should give the show a try. It has amazing storytelling with well-rounded, complex characters in complicated situations and doing what they have to in order to survive; and the story is all about the characters, their relationships and their personal arcs and developments, about trust and betrayal and questioning what it means to be human, understanding the morality between human and a free-thinking, breathing, feeling machine entity. It's just, I can't gush about it enough. In my opinion, it's truly phenomenal and one of the best epic science fiction television series I have ever watched. So yeah, I highly recommend it to everyone who has yet to experience how frakking awesome it is.
Honorable mentions: Firefly and Terminator: The Sarah Connor Chronicles are of the same vein, amazing science fiction shows that have affected me in a particular way and that everyone should watch.