PHPSiteStats is a free web application for monitoring traffic to your site when you do not have access to your server logs. It works by generating its own logs, and storing them in a text file or database to your specification. The GD-generated charts in the reports also look very nice ;-)
Updated 2021 : note that the above post is out-of-date, given this post was originally published in 2004, but is left here for archival purposes. The old link for PHPSiteStats, http://phpsitestats.sourceforge.net/, seems dead now so I have unlinked it.