Movies are as old as psychoanalysis. So if I were to put you or anyone else on a couch and say, ‘Tell me your favorite movies,’ it would be a way of psychoanalyzing you. 
Andrew Sarris, regarding movies as therapy

Although I’m not sure I follow the logic in the above statement, I do believe that long-time movie critic Andrew Sarris, who died last year at the age of 83, had a point about favorite movies reflecting one’s inner world.

In a 1998 interview with David Walsh, Sarris elaborated further on this theme: “Film has everything. I think it’s an emotional medium, above all. Anyone who depends on movies to educate himself, I think, is on the wrong track. What you derive from a film depends very much on what you bring to it. It allows you to focus emotionally on things you already know. It brings things to a point. Like music. Film is the art to which all other arts aspire. It produces the most sublime emotions.”

And because they do so well at bringing out various emotions, it’s true that movies can be useful as an adjunct to therapy. One therapist who actually specializes in movies as therapy is Dr. Birgit Wolz, who wrote E-Motion Picture Magic: A Movie Lover’s Guide to Healing and Transformation (2004).

She conceptualizes three types of cinema therapy:

1. Evocative: when a client raises the topic of having seen a certain film, Wolz can look at what the characters or scenes evoke in him or her
2. Prescriptive: based on a client’s presenting problems, a certain movie may be prescribed as a learning tool
3. Cathartic: when a certain film enables a client with blocked emotions to laugh or cry or both

Her website offers a lot of good stuff, including guidelines for film-watchers and for therapists, special articles and links, movie reviews, and a list of films organized by the types of issues they represent.

Likewise, you can click on the Zur Institute website for a comprehensive list offered jointly by Wolz and psychologist Dr. Ofer Zur.