[DavidPiper]

Seconding: Paprika was amazing (and hard to avoid comparing to Inception, which came out a few years later). Millenium Actress and Perfect Blue are burning a hole in my bookshelf - still haven't got to them.

Also seconding Your Name - hits the whole emotional spectrum, even on second and third watch when you know what's happening.

As lesser-known recommendations from Ghibli, I think Porco Rosso and From Up On Poppy Hill are both underrated-and-good in their own way, though they don't quite leave the impact that some of the others do.