There are a number of site analytics tools being offered, some for free. So which is the best one? My experience has shown Google Analytics to be one of the best. Their member page breaks down the data by many categories, but I find the following to be most useful:

Visitors
This captures all visitor related data such as Visitor Trending and Visitor Loyalty (very important in my opinion):

Visitor Trending: Includes Visits, Absolute Unique Visitors, Pageviews, Average Pageviews, Time on Site, Bounce Rate and New Visits

Visitor Loyalty: Includes Loyalty, Recency, Length of Visit, Depth of Visit

Traffic Sources
Equally important, this captures the sources from where your visitors reach your site. The most important being Direct Traffic, Referring Sites, Search Engines and Keywords.

This is the best website analytics tool that's being offered for free. It breaks down what's important and lets you see who visits your site, when, how often and where they come from. No one else come close, not for free anyway. Others offer limited resources that can be helpful, but charge a fee for the full feature.