I use a freeware counter called VersaCounter. It works pretty darn good. Thanks for the code Chavel!
On most of my pages, a "visit" is defined as a unique IP address over a 4 hour period. This isn't precise, sometimes it gives false positives, sometimes false negatives. But it gives a reasonable estimate. It's actually a non-trivial exercise to figure out exactly how many folks have visited your site.
I made a simple port for Versacounter so that it works with .png files instead of .gif files. See my 12-6-03 Journal article.