I once heard a word, derived from Latin or Greek elements, construed to describe a person who has an obsession with being published. What word might that have been? For example, what would you call some who has an inexplicable need to blog?
Someone who is obsessed with writing is a graphomaniac, from Greek graphein, "write", and mania, "madness":
One who is constantly writing, either letters to friends or to the newspapers, or stories and works of fiction, driven thereto either by an exaggerated idea of the importance of what he writes or by an insane impulse.
To round it up, here's a link to the Wikipedia article on graphomania:
Outside the psychiatric definitions of graphomania and related conditions, the word is used more broadly to label the urge and need to write excessively, whether professional or not.
That being said, as far as blogs are concerned, how about blogomaniac? You probably won't find it in any dictionary (yet), but it is pretty much self-explanatory, and as a free bonus, it sounds and looks very similar to logomaniac, someone who is obsessed with words or talking, from Greek logos, "word".
Blogomaniac in RegDwight’s answer is fine, but another option is blogaholic or blogoholic.
A person with an inexplicable need to blog might also be defined as having OCD, or someone who really lacks an otherwise constructive hobby. That said, at its core, blogging is merely writing in electronic form, so "graphomaniac" is a sufficiently good choice. Logomaniac wasn't in my MW dictionary, so I won't comment on it, except to say, please, everyone, let's not coin one more internet-centric term.