Perfect Blue | Check it out if you can

This is one of the best anime movies I've ever seen. It's a psychological thriller about a pop star, who decides to quit singing and start acting, but it'd seem that one of her old fans doesn't actually dig the idea and corpses start to show up. In the end, the film becomes quite disturbing, as reality and fiction start to become blurred.

Truly a great flick, and I recommend it to anyone interested in these kind of movies. Even non-anime fans.