I'm going to go with Spirited Away not only because it is an impossibly beautiful coming of age story that is rooted in Japanese culture, but ends up drawing attention to the universiality of human experience (that is a mouthful), but because it has always seemed to me like a gateway drug into the world of anime.
Even my friends who insist they hate anime, or as my sister calls them "sweaty cartoons," enjoy this film. The characters are complex and loveable; there is drama, pagentry and fantastic storytelling; the artwork is phenomenal. This film does have the ability to change some viewers' preconcieved notions about the purpose, scope and audience of anime.
This film has won 35 awards, including an Oscar for Best Animated Feature in 2002 against 4 American films Ice Age, Lilo & Stitch, Spirit: Stallion of the Cimmaron, and Treasure Planet.
Everyone should see this movie.