Wordpress.org is easily the most popular free/open source option out there, for blogging or even general websites. People like it because it makes it very easy to install, and use, even if you are not technically inclined. Wordpress.com (not to be confused with Wordpress.org) allows you to create free accounts, hosted by them. In addition, almost every shared host (Dreamhost, hostmonster, etc) have one-click Wordpress installs.
There are other options like Drupal or Joomla that allow you more control over what you can do, but this usually comes at the cost of usability for the person that has no desire to learn any sort of coding (e.g. photography, cooking blogs).
In addition, Wordpress has a wide variety of ancilliary benefits that come along with being the market leader, including:
- Large plug-in support
- Variety of free and paid for themes
- More questions that have already been answered online
- Greater familiarity with developers