I made a post 3 years ago which I will modify for this posting.
Anime movies I have seen that I think are worth watching:
everything Studio Ghibli, top popular opinion: Princess Mononoke or Spirited Away. Personal favorite: Porco Rosso
everything Satoshi Kon, top popular opinion: Paprika. Personal favorite: Tokyo Godfathers (probably also Paprika, actually, but I felt like Tokyo Godfathers deserved to be called out as it's exemplary)
everything Makoto Shinkai, top popular opinion: 5cm Per Second. (There's huge buzz for Your Name which is doing very well in Japanese theaters right now. It's not available outside of that though) Personal favorite: The Place Promised in Our Early Days. (Actually my absolute favorite of Shinkai's works is She and Her Cat, but as it clocks in at about 5 minutes it's not quite long enough to be in the running)
everything Katsuhiro Otomo top popular opinion: Akira. Personal favorite: Memories.
everything Mamoru Oshii top popular opinion: Ghost in the Shell. Personal favorite: Angel's Egg. (I don't actually like Oshii much)
everything Mamoru Hosoda, top popular opinion: Wolf Children. Personal Favorite: Girl Who Leapt Through Time
all seven movies in The Garden of Sinners series
Mind Game
Anthem of the Heart
Redline
Genius Party and Genius Party: Beyond (which, despite airing theatrically as one film circulated the internet as a bundle of separate short film files)
Tekkonkinkreet
INTERSTELLA 5555 (essentially a glorified music video for the Daft Punk album Discovery)
Ninja Scroll
Royal Space Force - The Wings of Honnêamise