Loren talks about his experiences with his ink blog.
Personally, I don't think that a blog entirely in ink is a good thing.
A weblog is certainly a form of personal expression, and it might be said that seeing someone's handwriting helps make it a little more personal.
But printed text is just easier to read. Would you want to read a handwritten novel? Even with the best handwriting (or your own handwriting), it's not going to be as easy to read, especially if the author is jotting something down quickly. You already have people who don't have the same native language trying to understand what you wrote, and now you're going to make it even harder for them (and everyone else) by making them decipher your handwriting too?
(Not to mention the increased bandwidth expense for everyone if we're transmitting images and not text - although I imagine things like SVG could help mitigate these concerns).
I do think that ink has a place in blogging, I just don't think it's a replacement for printed text. There have been many times when I thought that a particular idea would be much better conveyed through a drawing or being able to circle something on a picture and annotate it.