Site Tracker
Simply sign up free, insert a snippet of code in your page, and you're on your way. They provide you a link to your personalized statistical reports page, that you can access from anywhere in the world through a web browser.

Site Stats
Site-Stats is a free counter/tracker service available to anyone who owns and/or operates a web page.

Digitmania Counter Software Sources
These seem to work well but if have the ability to install new CGI scripts on your WWW server and want to do it your self.

WebLog
By Darryl C. Burgdorf, WebLog is so well documented you can learn how to do it yourself. They also offer several other useful scripts, Download the whole archive it's a all under 200k.

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Advanced Traffic Auditor

eXTReMe Tracker
We are currently using the free version of this system, to get a demo just click on the icon at the very end of my page. Every advanced feature required to understand your visitors of your web-site. numbers, percentages, stats, totals and averages. All the way up from simple counting your visitors until tacking the keywords they use to find you.

Live Counter
Live Counter was first to offer an access counter able to update its hits display as you watch. Now their Live Counter plug & play brings you more firsts.