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.

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.

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.