I had never run a counter, relying on feedback and actual results in the form of sales to gauge traffic. Unfortunately this told me little about who was visiting, why some were more interested in our site than others, why some people explored further to the point of making a purchase and others didn't. The tracker I chose was Hitbox. One of the main features of Hitbox is that it gives a good count of actual visitors, rather than 'hits'. This adds up to a very useful service, although it is too early to see all the trends.
Some trends are obvious, though.
I have always designed websites aimed at the 'lowest common denominator', being a screen resolution of 640X480. I have always used 24 bit colour though, as most of my sites are heavy in photos. I check all pages with a 256 colour palette though, to make sure that they are not too ugly. Hitbox gives a breakdown of the screen resolutions and colour depth of visitor's systems. To me this means that I can now aim for this resolution when designing for the web.