I know this answer is 5 years too late...

To update your favicon image you have two options: 
1. Place the desired `ico` image in your `skin/frontend/<package>/<theme>` directory (as suggested by St3phan above)
2. Upload your `ico` image to the `media/favicon` directory and create a `core_config_data` row with a value pointing towards it.

You can look at `app/code/core/Mage/Page/Block/Html/Head.php` `_getFaviconFile()` to see how the favicon file is loaded. Also note that the Head block will check the media directory first and looks for the file specified in `Mage::getStoreConfig('design/head/shortcut_icon')` before it checks the skin directory. Also note that the skin directory version must be named `favicon.ico`.

While there is the `System->Configuration->General->Design->HTML Head->Favicon Icon` field you can supposedly use to update your favicon image, it does not work for `ico` files. This is due to the validation that is run during the save process in `app/code/core/Mage/Core/Model/File/Validator/Image.php` which calls `imagecreatefromstring` (see https://www.php.net/manual/en/function.imagecreatefromstring.php) which will always return false because it does not support `ico` files.