Casablanca was the film that did it for me.  After that I wandered to see Lawrence of Arabia, Schindler's List, Apocalypse Now, Dr. Zhivago and that did it.  My obsession began, and I set out to see all of the AFI's 100 greatest films.  After that I wandered to foreign films, with the first two being Wings of Desire and M.  Since then the obsession rarely stops.  The most recent film to leave me stunned was Bloody Sunday, powerful stuff.