This is one that has been bugging me since the start of 1.5, but I can take no credit for it. I have found the answer in a joomlart.com forum from mj1256, but do want to share this with all of you.
Yes, it does work to create a favicon.ico and put it in the root of your template folder. And then one day you want to change it. Clearing cache does not help – changing the code does. Enough waffel, you all have waited long enough.
As per mj1256 on joomlart.com
create your favicon.ico with an ico editor – or name it what you like eg. myicon.ico
then up load to your media directory
add this to your templates header – that is go extentions, template manager, click on your template, click edit HTML and add the line below your
and walla, immediate update to your new icon file! Done and dusted and this can now be put to sleep! If you want to change it, call it what you like. You can name your icon myicon.ico or what ever you like, just change the code accordingly and you icon will change on your next click!