In most cases they provide little useful information. For the same amount of effort, a complete third-party tracking system could be installed. In one case, a friend who is the executive director of an organization was excited by the significant increase in users reported by the counter, and failed to understand that the same robot was visiting the home page every 6 minutes and was being counted 1,000 times per day. They will report number of unique users, repeat users, pages displayed, and referrers. They can be free if you display their logo on the pages.
Every server records every action into a log.
Depending upon traffic, these logs may be maintained on a daily, weekly or monthly basis. We recommend a monthly analysis of the logs to get a perspective on activity. I use Analog, which is free. Next month when we discuss these programs I will show some screen shots from WebTrends live and a report from Analog. Definitions are critical to understanding websites.