Fenxy

Graphics? Art you mean? They used to be hand drawn you know :)

I'd vote for Princess Mononoke, Nausicaa, Howl's Moving Castle, Tokyo Godfathers, Millenium Actress, Akira...

I know there was a note like this somewhere around, but I can't find it anymore, just its variations. If I had to pick my top animes, graphics would come second though, but here's my list if you were to include graphics as well:

Vandread (First and Second Stage)
Last Exile
The Melancholy of Haruhi Suzumiya (pay close attention to the famed God Knows music scene, it has the highest FPS in any anime).

If it was just the storyline above all else:

Full Metal Alchemist (still my number one favourite anime)
Neon Genesis Evangelion
You're Under Arrest (women in uniform, how could I not resist?)

I would second Vandread (1st and 2nd stage), and I'll add Ghost in the shell S.A.C, and both seasons of Honey and Clover.

Nothing is prettier than Ghost in the Shell: Innocence, but the storyline was a little challenging.... and I'm a Shirow worshiper!

I have yet to see an anime film that blew my mind more than Akira did. It hold up exceptionally well for being, what... 20 years old?

Final Fantasy was a mess on the big screen. Incomprehensible plot with zombie scientists as heroes. What were they thinking?

On the small screen, Cowboy Bebop is my hands down favorite, with the eerily similar Samurai Champloo a close second.

Again, I love Shirow, but the GITS anime runs were merely awesome, not life-changing.

flcl, spirited away or champloo

i love gainax's frantic style of fight and blending of different art styles. and bebop/champloo really needs no explination.

spirited away is a masterwork, and should be seen by every anime fan

Utena
Cowboy Bebop
Fullmetal Alchemist
Card Captor Sakura
Champloo

Based on storyline and art?

Cowboy Bebop
Princess Tutu
FLCL

howls moving castle for Art
DBZ For story(THE SHOWS A CLASSIC)

But Full metal alchemist is def my fav

I could never say that a single anime was my fav so I had rather make a top list...

1. Kino no Tabi(Kino’s Journey):
This episodic anime left me jaw dropped after every episode. Genius… The scanlines in the scenes gave it a nice feel

2. Battle Fairy Yukikaze OVA:
Some of the best CG animated sequences ever.

3. Full Metal Alchemist:
Sugoi! Sugoi! Along with the movie it is conceptually one of the best!

4. Samurai Champloo:
Shinichiro Watanabe is a genius! Unique animation style, music and grim side of the story telling along with the humor makes it a must watch.

5. Black Lagoon:
Grim portrayel of modern day evils. And obviously, Revy turns out to be one of the hottest anime chicks! ^^

6. Rurouni Kenshin OAV - Trust and Betrayal:
I have seen the other OAV as well as the series. But, this anime left me with nothing to complain about. 4 episodes of sheer anime pleasures.

Others
- The Melancholy of Haruhi Suzumiya
- Last Exile(this too)
- Hellsing OVA

Wolf's Rain

Here's the top ones that come to mind:

Utena
Fushigi Yuugi
Castle in the Sky
Grave of the Fireflies
Cowboy Bebop
Berserk
Nausicaa
Nadia Secret of Blue Water

I'd say all have great animation, story lines, great characters and amazing music. I haven't seen anything new in a few years though, so these are all older ones. Initial D is another favorite, but i'd say it's more entertaining than "Great".

Full Metal Alchemist for the story, still a fantastic tale, Mononoke too, but in terms of looks, Champloo or the Ghost in the Shell works. Hot stuff.

Akira, Ghost in the Shell, Appleseed, Black Magic 66, Ninja Scroll.

Yeah, I admit it, I'm old school.

Serial Experiments: Lain
Last Exile
Cowboy Bebop / Samurai Champloo
Ghost in the Shell
Anything by Ghibli :)