Changing the Favicon in SharePoint is very easy.
1. Create your icon and name it ‘favicon.ico’
2. Go to the path on the server below and back up the original icon.
3. Save them both somewhere to be able to be used at a future date, if necessary.
4. Copy/Paste your new favicon.ico to the path.
5. If it doesn’t show up immediately, it could be cached, so press Ctrl-F5 or use your Browser Tools to refresh the cache – voila!

C:\Program Files\Common Files\microsoft shared\Web Server Extensions\15\TEMPLATE\IMAGES (for 2013)
C:\Program Files\Common Files\microsoft shared\Web Server Extensions\14\TEMPLATE\IMAGES (for 2010)