Drupal FAQ: How do I set the favicon.ico icon file for my Drupal website?
There are a number of ways to do this, but one of the best ways is through the Drupal admin interface. From there you can upload your favicon.ico file and it won't be clobbered whenever you update your Drupal website.
To add a custom favicon.ico file to a Drupal 6 website, go to Admin > Themes > Settings, which in the case of one of my websites using a version of the Austin theme resulted in this browser path (URI):
If your theme is named 'foo', your path will be:
From there, the easiest way to upload a custom favicon.ico file is to use the "Upload icon image" field (not to be confused with the "Upload logo image" field). Just upload your custom favicon.ico file to your Drupal 6 (or Drupal 7) website, and you should be in business.
Note that depending on your website settings you may need to clear the Drupal cache. You can do this by clicking the "Clear cached data" button on this page:
How to create a favicon.ico file
If it helps to know it, you can create a favicon.ico file using Gimp. Just create your file as something like 32 by 32 pixel image, and then save it with a ".ico" file extension. Gimp is smart enough to figure out that you want to create an icon file.
Custom Drupal favicon.ico tip - Summary
I hope this tip on setting a custom Drupal favicon.ico file has been helpful. As usual, if there are any questions, just use the Comments form below. For more information on "Favicon" icon files, see this Favicon Wikipedia page.