my fav anime

[Kitten]

What, no Howl's Moving Castle?? That's my favorite one!

Heh, I completely forgot about Digimon Tamers. That was one of my early furry influences.

Cencoroll, short film, also pretty good. Sort of like a dark take on Pokemon.

I like ALL the Miyazaki/Studio Ghibili movies.

Tho another great anime movie is Paprika.

[Tyins Darkwulf]

I'm not really that big into anime anymore but I still have a few favorites:

.Hack//Sign Opening
(Not a lot of people like .hack//SIGN but this is the only anime series I can watch multiple times.

Read or Die Opening
(If you haven't watched the Read or Die OVA, seriously stop what you're doing and watch it. It's amazing.)

Miyuki-Chan in Wonderland Trailer
(Miyuki-Chan in Wonderland is so hilarious with total lesbian erotica undertones throughout the whole thing lol)

Escaflowne: The Movie Trailer - Bandai Entertainment, Inc.
(The Escaflowne movie is a re-envisioned version of the anime series storyline. I prefer it over the series by far)

[starflier]

Couple things came up in this thread that I want to watch now :D
I don't watch a lot of Anime, But these are the ones that I've spent significant time on:

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Slayers is a hilarious, fantasy show that feels like somebody's drunken D D campaign.

<iframe width="560" height="315" src="http://www.youtube.com/embed/SUjiXriGFbo" frameborder="0" allowfullscreen></iframe>
Last exile is pretty awesome, it's got a whole deiselpunk, Talespin thing going on. It kind of falls apart near the end when the male lead suddenly (like within one episode) gets romantic subplots with every female character. And then they find a spaceship that flips the world upside down. Yeah.

<iframe width="420" height="315" src="http://www.youtube.com/embed/o3b0A_KjihY" frameborder="0" allowfullscreen></iframe>
FLCL... Is pretty weird. I don't have much else to say about it. It's got some awesome fight scenes though

<iframe width="420" height="315" src="http://www.youtube.com/embed/NA3tyjq34MA" frameborder="0" allowfullscreen></iframe>
Rocket Girls is the most realistic hard science fiction I've ever seen on television. Even if the character motivations are a little weird...

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Not Japanese, but there's enough anime influence that I think it counts...

[Hadlock]

Bust Through the Heavens with Your Drill!!

Casshern Sins (SUB) - 1 - At the End of the World

:3

[Zelminax]

so many good anime's mentioned so far.

a few of my favorites to add are: any Gundam from mobile fighter G and gundam wing till most recent.
The opening of gundam00 (link--->  <iframe width="640" height="360" src="http://www.youtube.com/embed/YHsXoX2IsTY" frameborder="0" allowfullscreen></iframe>
Wolf's Rain is a great shorter anime: http://youtu.be/xoQuu7GPxAI
a classic that i still love to watch is Final Fantasy: Spirits Within.

(couldn't get the embedded youtube video to work and didn't want to spend a long time trying to figure it out on my own.)