Popular sites receive high concurrent web visitor requests and some clients send bad favicon.ico fetch requests. If you are running nginx you probably didn’t notice that, for example: /category/favicon.ico generate significant 404 errors in your server error log file, because this file is located only in root, e.g. /favicon.ico.
Every request for non-existent file takes some load and every 404 missing file error is usually logged into error_log file, unless you have disabled error logging. To forward all non-root favicon.ico requests to /favicon.ico you can set-up the following rewrite rule in nginx.conf file in the correct server{} location:
rewrite ^/(.*)/favicon.ico$ /favicon.ico last;
Voila. Restart the nginx daemon and you will see slightly decreased load on your box.