What iPad apps are available that support handwriting recognition?
You might like to checkout Writepad - it sounds like it does pretty much everything you are asking. I've used it before, and found it worked pretty well. It's only $4.99US at the moment as well, so maybe a good time to give it  a go.

I also use Plecodict which is an English-Chinese dictionary, which has handwriting recognition for learning new characters (and an optical recognition mode as well) - just mentioning it because you didn't specify a certain language.

Good luck.