I never got into series really (aside from Eva and Escaflowne), so my picks will be movies. Hopefully some of these are new to the pile of recommends.
Wings of Honneamise
1987
An alternate history earth (or other planet entirely can't remember) that's undergoing its space race to put the first man into orbit. Incredibly detailed world design catered to the culture's architecture, fashion, religion, and customs. Funny, somewhat of a tearjerker, and poignant without seeming preachy. The ending is one of the most memorable I've seen from an anime, heck, a film.
https://www.youtube.com/watch?v=2fcvUrhFEpk
Pom Poko
1994
Directed by Isao Takahata, director of Grave of the Fireflies, yet a drastically different tone than the former. It's extremely light hearted and wears its goofiness on its sleeve, so if the idea of Tanukis that shapeshift using their ballsacks sounds too absurd for your enjoyment then you may want to move along. It's one of my favorite Ghibli films, a lot of that due to the lazy afternoon pacing. The transformation sequences are animated wonderfully, and have a kind of magical realism to them I haven't seen conveyed as well in most other animated films (perhaps only rivaled by Ponyo). This really is a wonderful film OP and I'd highly recommend it.
https://www.youtube.com/watch?v=SAfqTDoqX98
Angel's Egg
1985
This is more of an abstract piece, a little over an hour, but a really unique experience for anime imo. Minimalist dialog, most of it is pure imagery with an atmospheric soundtrack. Certainly something that opens up your imagination a bit and lets you fill in the blanks for the main character's backstory, what has happened to the world she is in etc. One of my favorites due to just how unique the overall feeling and tone is.
https://www.youtube.com/watch?v=r04X-ImELzc
Cat Soup
2001
A half hour short that's about as weird as they come, but if you're open to the more surreal stuff you may dig this. Some really unique imagery here, but definitely not a standard narrative.
https://www.youtube.com/watch?v=jWy2E36k0hs
Paprika
2006
In my top five easily, it's psychadelic, mind bending, and has some of the best cel animation I've seen. All about dreams, technology, and the crazy shit that can happen when you mix the two together. Unforgettable, just watch it.
https://www.youtube.com/watch?v=jJzEW_eE1G0