If you liked spirited away, you may enjoy some of Miyazaki's other films. You can wikipedia him and watch the films chronologically and watch how the art styles develop. It's also really interesting to note the parallels between many of his films. This list below is NOT the chronological order, it's just films that I liked. None of his films are necessarily linked by storyline or characters, I'm speaking from a pure appreciation of how well all of his films are drawn.
Laputa: Castle in the Sky
Kiki's Delivery Service
Porco Rosso (my favorite from Studio Ghibli)
Howl's Moving Castle (second favorite)
Princess Mononke
Nausica
My Neighbor Totoro (my least favorite, but there is a funny story behind this; It is a a light-hearted children's anime and was first aired with Grave of the Fireflies as a double-feature. I can't imagine bringing a child to see Grave of the Fireflies)
And here are other anime that I really enjoyed
Samurai Champloo
Scrapped Pincess (I don't think anyone mentioned this yet, it's superb)
FLCL
Full Metal Alchemist
Full Metal Panic (pretty good mecha anime, only watch it so you know who everyone is in Fumoffu and Second Raid)
Full Metal Panic: Fumoffu (pure comedic genius)
Full Metal Panic: The Second Raid (epic overall)
Negima (I was forced to sit through Mahou Sensei Negima, which is nothing but a trashy ecchi anime, but Negima is a polished remake that might turn out to be pretty cool although I've only seen a few episodes so far)
The redone version of Hellsing (I think it's called Ultimate Hellsing, it's a series of OVAs still in prodction) has been fantastic so far. It's definitely a little more gore than the original anime series, but the storyline and visual effects are excellent and worth checking out.
And the best anime of all time is Azumanga Daioh. You'll either love it or hate it, but it's quite hilarious.
Here's the review I found on Azumanga Daioh's wikipedia page, I feel that it is accurate.
In Japan, the Azumanga Daioh manga received a Jury Recommendation during the sixth Japan Media Arts Festival in 2002.[11]
English reviewers have commented positively about Azumanga Daioh. Fred Patton of Animation World Magazine, has described Azumanga Daioh as "delightfully witty and even an educational window onto what Japanese high school life is really like."[12] Chris Beveridge of Anime on DVD, stated that "There's a lot to laugh with here and a cast of characters that grow quickly on you as you start finding those you favor and those you don't."[13] Andrew Shelton from Anime Meta explains that "The character of the girls (the only male is the rather creepy Kimura-sensei who has a, thankfully, minor role) is extremely well brought out. The superb observation, and ability to capture expression, makes the anime incredibly fun to watch in addition to meeting the story requirements. The action, and very rich comedy, are also wonderfully represented. There is just so much meaning, and charm, in even the most minor of expressions."[14] The licensed manga had sales that reached top 100 lists on occasions[15] and was included in the top 25 manga recommended by International Correspondence in Retailers Guide to Anime/Manga.[16] The English dub for the show was well received, earning 6 ADR Awards from fans voting on AnimeonDVD.com and Dubreview.com. Volumes 3, 4 and 6 won "Best Dub of the Month" and Allison Sumrall (Kagura), Kira Vincent-Davis (Osaka) and Christine Auten (Sakaki) won individual "Best Actress of the Month" awards.
Four of the girls were included in Newtype Magazine's top 100 anime heroines of 2002: Osaka was awarded 7th, Chiyo 11th, Sakaki 21st, and Yomi 78th. Together they made Azumanga Daioh the second most popular series of 2002 for female characters.