If you want to run a blog without using one like blogger or the other hosted ones you can run your own blog software if you have some webspace that people can access.
try: http://www.opensourcecms.com
They let you play about with lots of different open source (i.e free!) software before you download and install it on your own webspace, they have quite a few blogs to try.
Very handy if you want to look into the various options out there.
