I was just going to say Gurren Lagann but I skimmed the thread and saw a couple of people mention Steins;Gate. That one's probably more along the lines of what you're looking for.

But seriously you need to make your way around to Gurren Lagann eventually. I can't get enough of it, and I don't even watch much anime.

Start by watching Card captor sakura.

Then if you like it, congrats', you're an otaku.

If not, well, you're not.

Bleach definitely, although anime stopped for the moment

Great thread people, I have watched a few mentioned. Reading some recommendations here I need to check them out. :)

Full Metal Alchemist - Kinda like Dragon Ball, but a bit more adult themed (surprising since the main character is 12), and only 50 episodes long.

Code Geioss (however you spell it) - Really good, 100% War and conspiracy, and a bit of a mindf**k

Death Note - Another Short and sweet Anime

Elfin Lied - Was blocked from USA/Canada due to the amount of blood and gore. Very Dark.

Claymore - If Fire Emblem were an Anime, this would be it.

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As a break from the serious animes

Black Lagoon - 100% Action

High School of the Dead - Poorly rated, but funny as hell

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Avoid One Piece, Bleech, and Naruto. a) Those are a bit childish b) They are long, One Piece is already twice as long as DBZ with no end in sight.

Quoting this for more visibility.

Cowboy Bebop is one of the best to start with anime. No silly stuff, funny at time, emotionnal at other times, incredible sound track.

Won't take a lot of your time, 26 episodes and a movie.

If you like war i'd seriously recommend utawarerumono for it's series of escalating battles.

Oh wow, I can't believe I forgot to mention this one, I agree with it, I actually think this was my first anime outside of DBZ.

Mind you it is a bit old, video quality is comparable with the Original Dragon Ball.

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Another good one is Ghost in the Shell

DEATH NOTE is the best starter to anyone who wishes to begin watching anime.
There's also the recent Attack on Titan, the last episode is just soooooo EPIC !

I would recommend "5 centimeters per second" really one of the best anime movies I ever watched. Than all the awesome classic movies from Studio Ghibli "Nausicaa of the valley of wind", "princess mononoke" and of course "Howl's Moving Castle" other really awesome animes are"The girl who leapt through time" and "Akira".