Another popular article on this site explains how to change your favicon in your Joomla! 1.0-powered site. Naturally, a lot of people want to know how to change your favicon in a Joomla! 1.5-powered site, so this article goes through the process of changing your favicon in a Joomla! 1.5 site.
The first article on how to change your favicon in your Joomla! 1.0-powered site covers what a favicon is and how to create a favicon, so I will not cover that information here. I will just explain how Joomla! 1.5 handles favicons differently than Joomla! 1.0.
In Joomla! 1.0, the favicon was stored in the /images directory of the site. The system automatically loads a reference to /images/favicon.ico in the header of a Joomla! 1.0 site, so you could change your favicon by simply replacing that file on your server.
Joomla! 1.5 handles favicons differently. Instead of having a central location for the favicon, Joomla! 1.5 loads the favicon from the root directory of whichever template is loaded on your site. For example, the template on this site is located at http://www.howtojoomla.net/templates/htj_960/, so the favicon for this site is located at http://www.howtojoomla.net/templates/htj_960/favicon.ico. If I wanted to change the favicon on this site, I would simply replace that file with a new file called favicon.ico.
Most template designers will either include the default Joomla! favicon in their templates, or they will include their own favicon. It is up to you to take the step of modifying your favicon.
As always, questions and comments are welcome.