Watched a lot in the 90's when I was a kid.
I liked:
Akira. One of the first big ones. Post apocalyptic, sort of like Japan meets Mad Max. Got me into motorcycles at a young age.
NGE. Was really way too young to watch something so fucked up, but it's great. Describing it would take too long but it's the thinking man's giant robot anime with some really involving characters + a Shakespearian tendency to gravitate towards tragedy.
Vampire Hunter D. Think gothic Castlevania / Dracula. Very old - early 80's I think. Hellsing is good too and came later, less serious in tone.
Bastard!! Nobody has seen this and it's just awesome
http://en.wikipedia.org/wiki/Bastard%E2%80%BC
Fist of the North Star. Really over the top and violent, but entertaining. Basically an 80's action movie.
That's what came to mind off the top of my head. And yeah anything Miyazaki is A++