Limiting myself to movies that stand alone:
1. Princess Mononke

The ghibli movie that resonates with me most. Naussica is a close second. Never liked the more children oriented ones.
2. Perfect Blue

It used to be fun making folks who had no idea what they were in for watch this. It probably wouldn't fly nowadays, but witnessing many a mind melt is forever etched in my mind.
3. Space Adventure Cobra

An absolute blast. Schlocky 70's style action. Cobra is super charismatic as a character.
4. Redline

A boy meets girl love story stuck inside of Anime wacky races. Steps on the gas early and never lets up. Visually a feast.
5. Promare

While I can appreciate the LGBT angle, the movie spoke to me in other ways. It's an incredibly positive film, and worth the time of anyone mildly curious.
Some honorable mentions:
Mobile Suit Gundam Trilogy

Equal parts history lesson and interesting military fantasy about robots and space psychics.
Akira

Seminal dystopian "don't create and abuse your super psychics" cartoon. Everyone should experience it at least once.
Utena the Movie

Full of bizarre visual metaphor, great looking action, and powerful messaging.
Wings of Honneamise

The origin of gainax. Follows some very flawed pioneers as they cobble together a space launch in a fantasy land.
Macross Frontier - The False Diva and Wings of Goodbye

Arguably the best Macross films. Unlike Do You Remember Love, these stand alone, and recontextualize and clean up the bullet points from the messy tv version.