Browsers store the favicon and it's one of the elements that is hard to refresh, even if clearing caches.
Here are some solutions to help with refreshing the favicon you see in your browser:
-ok I see @Lodders answer, there are the 2 first options I wanted to suggest, so below are a few other options by browser. Since I am on a mac, the solutions I propose are mainly for mac - and the 3 browsers I am most familiar with.
##Firefox:
Navigate to FF about:config page.
Filter with the term: browser.chrome
Set browser.chrome.favicons and browser.chrome.site_icons to false.
Close and re-open FF.
Re-set the above setting to true, to re-enable favicons, and force FF to download fresh ones from the websites you navigate.
For firefox there is also an addon that removes/clear favicons: https://addons.mozilla.org/en-US/firefox/addon/delete-bookmark-icons/
*I think this should be similar in Windows as well.
##Chrome Mac: Remove the file:
~/Library/Application Support/Google/Chrome/Default/Favicons
*There should be a similar location where Chrome stores local data in Windows.
##Safari Mac: In older versions, it was possible to select to remove website icons, from the Reset Safari command.
In recent versions, you can remove the file:
`~/Library/Safari/WebpageIcons.db`