But I think, sometimes it's a bit too much. First of all, not everyone wants to create an account at google just to see, how much traffic a site gets. Also today many customers don't like to see, that their habits get tracked by google. They want to have a small digital fingerprint. The last point is of course performance. Even if the google analytics script isn't that large, it's still some code which has to get fetched and evaluated.
To the rescue, every web server has something built in which is called an access log. This gets updated as soon as a user comes to your page or does a request on any resource on the web server. Now, this is one of the ugly files, no one wants to read. It's a simple text file, which shows all the requests line per line in a not very readable format.