Well, the thing is, I see it as a chore: I share my name with quite a few people, including two compatriots a few years younger than myself who have been convicted of violent crimes, so I like to watch how Google's result rankings shift around in the hope that someday it'll be harder to plug in my name and read the equivalent of 'VanishedOne killed a pensioner'.
Spending a lot of time on the Internet to see how often your name appears and what others are saying about you. It’s another way of saying 'Googling yourself,' although a narcissurfer does it on a daily basis.
Used in a sentence: "You’re such a narcissurfer. You probably think this blog is about you."