Last Exile
The first anime I had ever watched, so I may be a little bias, but it has really good characters, story, art style, and it all takes place in a sort of futuristic almost steampunk world with all sorts of cool flying vehicles. It'll take a good amount of time on the wiki afterwards to fully understand everything but it's highly worth watching, despite a slow start into the main plot

Generic hot-rod-guy-enters-race-to-win-the-girl plot, but its how everything is presented that makes this movie great. Every inch of adrenaline that the characters are feeling you also feel, the sound, the animation , the sheer speed, everything you feel resonating directly to you. Not to mention it also has a kick ass funky soundtrack, and a truly amazing comic book style that's characteristic of madhouse's animation. Give it a watch, it's worth it

Read or Die OVA
Very short but it's very good for what it is. Girl that's definitely not neurotypical and loves books must track down a manuscript stolen by some secret group using her ability to control paper with her mind. Unique concept and story, and great 2000s art too. Only complaint is needs more yuri

Perfect Blue
Psychological thriller about a parasocial attachment to a diva-turned-actor. Probably my favorite Satoshi Kon film as it actually cinematically integrates the "blending of dreams and reality" portion instead of shoving it in your face. (Sorry but Paprika was a letdown, cool animation tho)

Vampire Hunter D: Bloodlust
Another Madhouse movie. Extremely beautiful art and story. Takes place in a post-apocalyptic world in which gothic architecture and vampires have re-prevailed, complete with road warrior type bounty hunters competing with our half-vampire protagonist. The Movie runtime actually plays in it's favour, Hellsing was just too drawn out

Pop Team Epic
Pure shitpost humor, Short clips most comparable to robot chicken, but with 2 anime girls with overly detailed hands. So well crafted shitpost humor that I had to buy both the english manga

I'm not entirely sure what I was expecting but it turned out to be so much cooler than whatever I was thinking. There's an explosion every 20 minutes. My friend described it as "feeling like a live action movie" which puts it well. The color grading and composition is just so grande and cool.

Hells (2008)
Anime girl late for school bread in mouth hit by truck type deal but she gets sent straight to hell. There's a character named Hellvis. The story isn't the best in the world but it's got nuts animation that looks straight out of the manga. I also didn't know this until after watching it but it's officially dubbed by the team behind Hellsing Abridged and all that

Panty and stocking
Imagine the powerpuff girls, but for a much more mature audience. By the insanely talented artists that are now at studio trigger, panty and stocking is one of the best nonstop action animes I've seen. Too bad there's only one season even after 10 years

Princess Tutu
A little bit of a break from my usual stuff, tumblr was saying this was good and it was. Nothing extraordinary about it but it's a sweet story with nice characters. It took me too long to realize Ahiru meant a type of duck in japanese

Serial Experiments Lain
If you're on neocities there's a good chance you've heard of this one already. Confusing-ass mindfuck about the internet and how we're all connected and some little girl at the heart of it all, or something like that, I'm not really sure. Go watch it

Madoka Magica
I had gotten the "bad guy" spoiled for me ahead of time, but there's so much more that I wasn't expecting. Well animated, amazing story. Go into it with the intent to watch a magical girl story, 'cause after all, that's what it is