Statcounter
www.statcounter.com
Definately the best website visit counter I have seen. Statcounter offers a totally free visitor-stats service; you can add as many websites as you like and each one is given a log size of 500 entrys. Using the easy management page you can track your unique visitors and pageloads, where your visitors came from, what pages they looked at, how long they were on your site, what browser they were using and much more. Statcounter is such a comprehensive tool for visitor tracking it is a must for the serious webmaster.
If you want to keep a more comprehensive log of your visitors you can upgrade your membership to the paid-for service, this ranges from £4.50 to £15 per month and offers from 1500 to 25000 log entries and 250,000 to 15,000,000 pageloads per month.
Along with this great service there is also a Statcounter Forum where theres alwasys someone online who will give you advice about your statcounter projects, other problems concerning your website or just for a chit-chat!