Apache

You can exclude your IP addresses or/and the specific user agent of your browsers :

SetEnvIf Remote_Addr "127\.0\.0\.1" dontlog
SetEnvIf Remote_Addr "192\.168\.1\.4" dontlog
SetEnvIf User-Agent "meandmyself" dontlog

CustomLog ${APACHE_LOG_DIR}/mysite.fr-access.log combined env=!dontlog

You can customize you user agent in Firefox by setting the key general.useragent.override in about:config. Don't modify it too much or your browser won't be recognized and some websites will not work. you can just add a signature at the end, but avoid to put something related to your name for privacy reasons (the user agent is seen by all websites you browse). You can check your user agent with a website like http://whatsmyuseragent.com/.

With this method you can also avoid logging robots or some pages, but if you use a good and well configured log parser (like awstats) it will do this job (even for your IP addresses, but not for the user agent).