It is possible that you might like a favicon (yes the logo icon that is displayed in the browser tab) of a certain website. Now, normally most of the websites store it in the form of favicon.ico in the root directory of any website. So, you can just type in: http://domain.com/favicon.ico and download it when it appears in the browser.
But, not all the websites store it this way. If you find it hard – let it be done by Google. Just type in the following link in the web browser – and it will show you the favicon.ico:
To get the favicon for a domain, use
http://www.google.com/s2/favicons?domain=www.domain.com
To get the favicon for an URL, use
http://www.google.com/s2/favicons?domain_url=http%3A%2F%2Fwww.domain.com%2F
Replace domain.com with the actual domain from which you’d like to download the favicon from.