+1 to the Porco Rosso suggestion, one of my favorite studio Ghibli/Miyazaki films!
Another decent anime an old housemate got me into is "Evangelion".
It's one diminishing trait, for me, is that the main characters are all children, and the voice actors they get for children are high pitched whiney voices... I watched it in japanese w/ subtitles, and after listening to parts in the english dubbed version, it actually doesn't sound too bad in english. If you can get past the voice overs, the series is quite good.
The art/animation is superb and the storyline, although slow moving at times, is unrivaled. It's probably my favorite storyline of any anime
series I've seen. It has a very dark futuristic backdrop complete with mysticism, Armageddon, secret government societies and attacking "angels" (which are more like demons who come to destroy the world.).
Now I might as well tell you about "Preacher" the graphic novel series also...
While not an anime, or animation. This graphic novel is top of the line, and the best story I've ever read in my entire life. I can't think of anything I like more.
I don't spend money on graphic novels, manga's or comics... but after borrowing book 1 and reading it, I went out and bought the entire 9 book series for something like 90$ after tax, new. (It's all full color, which drives up the price a bit. But you can pick up the books much cheaper on ebay, used around 40-50$ for the complete set.)
The storyline involves the offspring of a demon and an angel, which once born causes God to disappear from heaven. The new entity dubbed "genesis" possesses a burnt out preacher by the name of Jesse Custer who subsequently decides to track down God and make him answer for all the evil in the world. the genesis entity is kind of benign (doesn't control jesse custer) but imbues him with "the word of God"... He can basically command people to do things with his voice, and they have no option but to do it. He's flanked by his two friends, one an ex-gf turned hitman (hitwoman?), the other is a 200+ year old Irish alcoholic/druggie vampire (the coolest, no frills vampire ever imagined.).
The series dabbles in Religion, Occult, Secret Societies, Black magick, and more... There are vampires, angels, demons, secret agents and more. It is extremely gory at times and at others just flat out raunchy and the art is just top notch. One of the books delves into the history of "The Saint of Killers" who replaces the angel of death, and is a complete western, with a different artist than the rest of the books and is an epic tale in an of itself. It's kind of hard to explain it all because it jumps around on so many topics and locals, but know this. It is the best of the best. Any comic/graphic novel store you go to will carry Preacher, and I doubt you can find anyone who has read it and doesn't highly recommend it to others. This isn't a book to show the kids, it is very dark and gritty.
Homer's Odyssey has nothing on the epic that is PREACHER.
