The script runs completely server-side - so there's no need to install anything on your computer. You can monitor your visitors via a browser, to see where they are, what pages they visited and how long they've been on your site.
Choose the script which suits your needs - from the Online Count which displays how many people are on your site, to the Users Online Pro which contains an admin section to view where people visited on your site, how long they stayed, a page to view where they are now - as well as logging search engine activity. There are a couple of scripts in between which are designed to suit your pocket.
Is security an issue on your site?
Do you have someone stalking your site? Users Online allows you to follow their path through your site, and you can then disallow their ip block through htaccess.
NO monthly fees.
NO software installed on your computer.
What do I need to run these scripts?
Your website needs to be able to run CGI scripts. SSI is the preferable method of calling the script, however you can use PHP or an image tag (the image tag does not carry referrer through on html pages).
Users Online Pro uses a mysql database, and uses DBI to connect to the database.