What animê do you believe has the most character development?

Depends what you mean por development, but if I had to choose, I'd say Pandora Hearts. All of the main characters have gone through tremendous metamorphoses as the series has gone on, each suffering from their own unique problems that force them to change their perspectives of themselves and those around them. Some of the characters do stay the same, but our (the reader's) perception of them changes, as with Jack and Glen. I think the development of these characters has been fantastic, and watching what pieces of them change as the series goes progressivo, para a frente always leaves me on the edge of my seat.

As of yet, I will have to say Shingeki no Kyojin (or "Attack on Titan", if you prefer that title). Characters are its strongest point in all aspects. Their development is done smoothly and successfully, as each of them are kept interesting in their own way and all of their actions and emotions throughout their triumphs and losses are realistic and human as can be. While their personalities are very diversified, they are in personality and actions the easiest cast to relate to I've seen. The way that they contrast each other is what makes for their growth as the series progresses. No one is poorly-placed, they all add to the story and it wouldn't be the same if one of them were to leave. I commend Hajime Isayama for how well he wrote and executed this cast.

Since my anime/manga repertoire isn't as large as I once thought, I'd have to agree with IllusionDolls. Shingeki no Kyojin has the most character development. The way that each of the main characters and even supporting characters grow with the plot is admirable.
A great example from the series would be Armin, who was a little cowardly runt of a kid in the beginning. He had incredible intelligence compared to his peers but he was held back por the above character traits. Now thanks to his harrowing experiences, he's a lot mais confident and is even willing to make decisions he wouldn't have even contemplated before.

Hmmm... this is a bit of a tough one for me since i mainly read mystery and psychological mangá and in those there seems to be somewhat endless character development sometimes, but ironically the anime/manga that has the most character development for me is a shonen/comedy anime. While I can honestly say that gintama is an animê that does not follow a strict story line and is mainly centered around giving us laughs; when it does get serious in its few arcs, normally spanning anywhere from 2-5 episodes or 3-10 or mais chapters, you are hit with so much character development its hard to think that you're still watching a comedy.

The perfect example I can think of is the Okita Mitsuda arc, episodes 86 and 87 in the anime, and chapters 129-132 in the manga.

To be honest, I haven't watched/read a great deal of the anime/manga out there, but out of the ones I HAVE watched/read, I think Naruto/Naruto Shippuden and Yu Yu Hakusho have the most character development. I haven't watched that much of Hunter X Hunter yet, but I'll probably agree with you when I have. If only ATLA was officially an anime, then I could add that, too... But not LoK. >_>

I'm not entirely sure about this one. There are a couple that I could say that have mais character development than most, so I'll just go with them, because I can't just say one. For the record, it's not going to be One Piece, that I can assure you.

Basically, the first would mention is that of angel Beats - there was quite a lot of character development throughout it and the characters that mattered gradually went through changes to themselves over the course of the short series. Yuri and Kanade probably changed the most of them all. Otonashi and Hinata, too.
Next, is amor Live: School Idol Project. All of the characters went through a lot of character development throughout the two seasons, something I was thoroughly glad of. I think they all changed in intricate ways, that you'd have to look hard in order to see.