Let's talk anime: What are some must-see anime movies?

After seeing the Spirited Away post and the 5 Centimeters Per Second post(which I watched and was absolutely blown away by), I'd love to know some anime movies you would all recommend!

For me, Grave of the Fireflies is an incredible animated film that is utterly devastating. Definitely high on my list of movies I would recommend to anyone.

How about you all?