I use Movable Type for my blog. They offer a free single-user license but you get no tech support for the free version. Your webhost also needs to have PHP (scripting language) and MySQL (for the database) for the blog to work.
Their site is: http://www.movabletype.org/
I guess I should add a link to my blog. http://www.webitude.com/debi/
Other free blog software include http://wordpress.org/
(these are the type you install on your own website, not the kind you sign up for like Blogspot, TypePad, or LiveJournal).