This is an extract of some of the open-source free blogging tools available in the market today. The Wikipedia article on Weblog software should give you a wider choice of tools to pick from.
 

Weblog software (also called blog software or blogware) is software designed to simplify the creation and maintenance of weblogs. As specialized content management systems, weblog applications support the authoring, editing, and publishing of blog posts and comments, with special functions for image mangagement, web syndication, and moderation of posts and comments. - Wikipedia

This list links back to the various application websites so you can download the software and try it out. The description in brackets also allows you to identify the environment you’d need to run these applications.

Apache Roller (Java-based)

b2evolution (PHP/MySQL)

PyBlosxom (Python)

Dotclear (PHP/MySQL)

Drupal (PHP/MySQL)

Elgg (Linux, Apache, MySQL, and PHP)

Geeklog (PHP/MySQL)

(PHP/MySQL)

Livejournal (Perl) (Also available, developer hosted)

LifeType (PHP/MySQL)

Mephisto (Ruby on Rails)

Nucleus CMS (PHP)

Pivotlog (PHP)

Serendipity (PHP/MySQL,PostgreSQL,SQLlite)

Slash (Perl)

Subtext (C#/ASP.NET)

Textpattern (PHP/MySQL)

Typo (Ruby on Rails)

WordPress (PHP/MySQL) - My personal favorite and the software that is used to run this blog.