Wordpress is good blogging software, very easy to use. It's popularity speaks for itself. Google have their own blogging service too, I think it's blogspot but not sure, I don't use it anymore since I have my own wordpress site running (not for blogging in the normal sense but for news updates etc for my business website).

Anyway, give wordpress a whirl, it's free, you can host it or they can host it for you. If you run in to problems drop me an email [email protected] and I'll see what I can do to help.