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Personally, as someone who isn't a fan of Anime in general, it would have to be the "Dragonball" franchise. While I still find the Anime version of "Z" to be too long and sometimes dull or ridiculous, I LOVE the manga, "Kai", and the movies, not to mention the classic "Dragonball", and I am now extremely fond of "Z" as an anime itself despite the filler. "Dragonball" was a show that I just never gave a chance when I should've.

The Guyver, at first the "monster of the day" thing kind of bored me, but the show started showing some real depth later on after the escape from Chronos.

Giant Robo seemed kind of average in the beginning, but around the 3rd episode someone decide to press the epic button and it got really juicy.

I didn't care for Fafner either, simply because I'm not crazy about the art, but I love how they make good use of all the characters in the series. It's a big accomplishment, character juggling doesn't seem to be an easy task for a lot of anime.

Narutard and Pokeymans

Kannozuki no Miko, Strawberry Panic and Utena (though hate's too strong for that one)

it took me quite some time to like Saint Seiya, as Athena and Seiya are as irritating as they come...

i do consider the fight and the circumstances surrounding Shaka's death to be among the best in anime though...

and Gemini Saga/Kannon = win!...

One Piece.

The art style really kept me away from it for a long time, but after grinding through the early chapters of the manga, I can't imagine how I ever disliked it in the least.

FLCL. Made no sense at all when I watched it. Then I watched it again, and it still made no sense, but I thought it was awesome for some reason.

Rama 1/2

I didn't care for Code Geass when I first saw it. Now I think it's worth watching all the way through at least once. It's hard to keep up with Gundam, Macross, and Evangelion, IMO.

Hokuto no Ken. First time I saw their design and Kenshiro's voice when performed hyakuretsu ken, I laughed hard. But not after I know his power, abilities, personality and the storyline. Now, Hokuto no Ken is on the top on my favorite anime list.

Death Note
so many damn people always talked about its greatness, and i didnt see how awesome it was till i actually started reading it myself

I didn't like Cowboy Bebop when i first saw it.
Keep in mind I was about 13 and even dumber than I am now. I now love the show.

Originally posted by XanatosForever
One Piece.

The art style really kept me away from it for a long time, but after grinding through the early chapters of the manga, I can't imagine how I ever disliked it in the least.
Yeah the more cartoony designs compared to the other animes id watched (DBZ, naruto & bleach) made all the characters look so much less badass.....not true when you get into it though (although i still like the more realistic art more).

naruto

Bleach. The first couple of chapters aren't great, then Ishida appears and shit hits the fans.

For a long time I absolutely HATED Naruto. Now I rather like it (mainly due to Hinata).

Originally posted by Endless Mike
FLCL. Made no sense at all when I watched it. Then I watched it again, and it still made no sense, but I thought it was awesome for some reason.

Wow, I was just about to say that when I came in here. Yeah, FLCL is weird and confusing as heck but still you gotta love the comedy and action in the series even if you don't know what's going on and why it's happening.

One Piece. I just got used to it and Toonami suddenly went off the air and One Piece hasn't been seen on television since. FML.

Neon Genesis Evangelion. The first time I saw it I was about 10 or 11 years old and couldn't understand a damn bit of it. Plus (with the exception of Misato, Asuka, and Gendo) I wanted to repeatedly punch every single one of the characters in the face. But now it's one of my favourite series of all time.

Originally posted by Anderson FTW!!!
Neon Genesis Evangelion. The first time I saw it I was about 10 or 11 years old and couldn't understand a damn bit of it. Plus (with the exception of Misato, Asuka, and Gendo) I wanted to repeatedly punch every single one of the characters in the face. But now it's one of my favourite series of all time.
Yeah I can see why you might not like it as well, it does take a little while to get off the ground and become worthwhile (it's entertaining for the first few episodes of course, but in a 'gundam' sort of way, not how it is later on).

Originally posted by Nephthys
Bleach. The first couple of chapters aren't great, then Ishida appears and shit hits the fans.

This is an awesome thing to say.

Originally posted by Mr. Rhythmic
Personally, as someone who isn't a fan of Anime in general, it would have to be the "Dragonball" franchise. While I still find the Anime version of "Z" to be too long and sometimes dull or ridiculous, I LOVE the manga, "Kai", and the movies, not to mention the classic "Dragonball", and I am now extremely fond of "Z" as an anime itself despite the filler. "Dragonball" was a show that I just never gave a chance when I should've.
Personally, I kinda not like (hate is a strong word, IMO) NOEIN when I first see it.
It's due to some science terminologies that I can't understand and the plot greatly confuses me up to episode 7-8.
But as soon as it reached episode 9 or so, I kinda like it more since the story is getting much better.

No wonder this is called an under rated anime.