Just for fun (and inspired by SotS), I thought I'd put in an anime top 10 list for the ongoing poll. My current list:

1. Spirited Away - Not only my favorite anime movie, but on my top 5 or so of all movies of any genre. Miyazaki's take on Alice in Wonderland set in a profoundly strange, beautifully detailed fantasy world. The only Oscar-winning anime to date (and let's face it, probably the only one that ever will win). And I'm sure even Chris will come around to its charms someday.
2. Giant Robo - Operatic in its scope. Exciting. Picaresque. And the world is over- and misused these days, but: EPIC. Yasuhiro Imagawa's blending of the best of Mitsuteru Yokoyama, flavored with Masamichi Amano's sweeping score makes for my favorite of all OVA series.
3. Haibane Renmei - A strange world where most things are familiar, but there is a strange twist to it all. Not-quite-angels living in a not-quite-purgatory. Great characters, great characterizations, profoundly moving. yoshitoshi ABe's masterpiece.
4. Kiki's Delivery Service - The first Miyazaki movie I ever saw, and I became an instant fan. A sweet coming-of-age story. It really feels like what growing up is like.
5. Cardcaptor Sakura - And this show is not what childhood is like, but what it should be like. Well, maybe not the dangerous magic (although nobody ever actually gets hurt), but the love and the friendship.
6. Fruits Basket - Starts off as a cute and perhaps routine romantic comedy with supernatural elements, with an improbably nice heroine: but then you realize this heroine is so good and so nice that she manages to melt viewer cynicism through her purity alone! And it ends with a gripping three-episode finale that tests her mettle to the utmost. Perhaps only a fraction as good as the manga, but I still love it.
7. Tenchi Muyo! Ryo-Ohki - The original 6-episode OVA only. As much as I love the rest of it, none of the rest of the regular anime franchise (with the possible exception of the third movie) can hold a candle to the original series, which remains an incredibly creative and beautifully designed science fiction story. Yes, it's derivative of Star Wars, Star Trek and Japanese mythology, but it's what it does with it that's interesting.
8. Gunbuster - I don't know if Gainax invented fanservice, but they certainly put it on the map with this great series. Funny, exciting, thought provoking. And frequently (but especially in the last two episodes), wrenchingly moving. I have never been able to watch the very end without tearing up. _______ ____, indeed.
9. My Neighbor Totoro - Being able to smile at this movie is one of the best things about being human. It's about being young and outdoors in the summertime in the country. When you are a child, there are millions of possible adventures. This is one of them.
10. Princess Tutu - Just as the west doesn't always 'get' anime, Japan doesn't always 'get' western culture. This is one series that so completely does. The creepy stories of ETA Hoffmann, the music of Tchaikovsky, Adam, Mendelssohn, Prokofiev and others, ballet scenarios, and fairytales are mixed together in a surreal Utenaesque manner to create a brand new fairytale.