I used to be SUPER into anime when I was finishing grade school and through most of high school. I watched and loved anything I could find. At some point though, I think between a combination of developing taste and literally just getting too much of the shit, I really backed off from it. I'm in my 30s now, so there has been a long enough break in there to where I've come to recognize what I liked was shit and what I genuinely love.
Like you I love the Ghibli stuff and the classics - Akira, GiTs, that stuff. The two shows that have withstood the test of time are without a doubt Cowboy Bebop and Macross Plus. They're both as good now as they were then. I still just adore those. You've gotten a ton of suggestions for Bebop, it's a must. I've seen other people say Samurai Champloo, which I found really disappointing. I think if maybe you watched it before Bebop you'd dig it, but from the 5 - 6 episodes I've seen it literally traces over too similar ground that Bebop covers. Some episode plots are nearly identical. I stopped watching it.
Another series I caught a few years ago and really liked was Mushishi. It's almost kind of like the X-Files of anime. It's super chill and has a great lead character. All self contained, interesting stories. Totally worth checking out a few.
One of my new favorites is Redline. It's a bat shit insane racing movie with unbelievable set pieces. It's one of the few movies (not just anime, all movies) that I wanted to watch again almost as soon as it ended. Just awesome.
Evangelion is a tough one I think. Only mentioning it since it got so many mentions here. It doesn't really get good until halfway through, and even "good" is a bit of an over statement. The show literally has zero likeable lead characters. Shinji, the lead, is unbearable. I was never able to warm up to him and as the show rolled on I only hated him more and more. Some cool ideas in there and a neat ending, but for me it wasn't really worth the pain of getting to those moments. It's a celebrated one, but I never quite understood it.
edit: I also have a bit of a soft spot for The Vision of Escaflowne still too. I've kind of been afraid to rewatch it because I don't want to possibly come to the realization that it's not good. But in my memory it's a cool show that kind of straddles the edge of shonen and shojo anime. Has amazing music at least, I still listen to those OSTs.