There was a time when my secret project, the thing that brought me in to work ever day and probably why I stayed till 8pm, was attempting to end the error_log from have anyone ever hitting the 404 page. It was after making the 404 page funny. Only no one got the joke.
If the below video does not work, then try Renny Gleeson: 404, the story of a page not found.
Eventually I did give up and focus on helpful things such that people could get where they needed to go.