I haven't watched that many anime series, but here are 10 that I liked. I think there are only a handful that I have watched that aren't on this list.... which probably means I really need to watch more anime ^__^
Hikaru No Go
Full Metal Alchemist (got a little too depressing for me, but still very good) Fruits Basket (good, but covers very little of the story) Inuyasha
honorable mention: One Piece (NOT the version with the lolipop instead of a cigarette, though... sheesh). I liked it but I haven't watched enough of it for it to replace something else on the list.
I was impressed with the understory in Howl's Moving Castle. The straight story is fun and very imaginative. The visuals are just YUM. I loved the Victoriana and it reminds me so much of Mary Poppins. It's a Disney production, and I think there was a tussle with the original director which I'm not sure about, and a retired director came on and took over the project. (I'm curious why all that happened.)
I loved the Ghost in the Shell series. An important comment about many anime films and episodes: the music alone is worth following animes. In this film, the song played during credits is highly atmospheric in the spirit of Raise the Red Lantern (Yimou 1992) which is a much more formal style and Chinese to boot. The singer during the GIS credit roll is a lot like Bjork. It's someone else though. The story itself swims in cyberpunk rock, very artfully and carefully placed. The city is a character in itself. Love that.
Probably one of my favorite developments in this series is the spider-like transformers in GIS: Solid State Society who are with the Section 9 attackers on the complex that houses the conspirators and the brainwashing project. The small transformers are visual comic relief in a pretty serious plot.
The whole thing is geared toward themes on justice and questions about identity. Some good stuff there to think on.
Princess Mononoke Oh my. Steeped in Japanese culture and history, almost all of which elludes me still. I would love to learn more about Japan, and I'm glad for a movie that inspires me with specific key points to investigate. This film definitely covers anime themes about ego and the wise use of power. Friendship is wonderfully portrayed here.
Final Fantasy Insanely gorgeous visuals in the movie and the game. I haven't bothered to follow the story one bit ... just basked in the wonderful eye candiness of it all. Massive storyline anyway.
Not anime but highly influential and bearing on a lot that happens throughout anything anime. Blade Runner.
Yes .... not a list of ten but I thought I'd put what's on the tip of my tongue. There's one that I was very interested in I haven't watched and can't remember the name of. That's typical of me. Not remembering names of things. Someone else recommended it here as well, so it's listed in this group somewhere. Anyway, that's what I've got for now.
Naruto - If you can sift through all the fillers it really IS a good anime. (Not that the fillers aren't fun.) Lovely Complex Ouran High School Host Club Honey and Clover Death Note -Not yet finished, but it has quickly become one of my favorites. Trigun Fullmetal Alchemist Vampire Knight RomeoxJuliet Fruits Basket
Hana-zakari no kimitachi e ( aka Hana-kimi. It's a manga. Never made into an anime *sob*)
Ouran High School Host Club ( that's a mouth full... )
Full Metal Alchemist
Inu Yasha ( One of my friends ranted about it being "Dragon Ball Z" for girls. And he's pretty much right. What girl would want to watch Dragon ball? It's a pretty long series, and everybody's fighting! *grumbles about stereotypical Shojo* )