Persona

Persona (1966)
[http://www.imdb.com/title/tt0060827/]

The Gist:
Ingmar Bergman goes Avant-Garde, creating a subtle piece of shifting identity. I've never been a huge fan of the avant-garde experimental genre, but when it's done right I can appreciate it. I can even like it, and perhaps I like this film so much because it still has a narrative thread. You don't get lost in the abstract meaning of it all, instead you're grounded by a simple reality. Here, that reality is an actress who has a breakdown, who isn't speaking, and the nurse who looks after her. After this is established you can start exploring whether or not they are the same person.