Each program or method has its different strengths, so a lot depends on what aspects you want to analyze. I have access to AWStats and Webalizer data, and also use Google Analytics, which is impressive, but the method I regularly use and rely on is to import my log data to a MySQL database. The downside is that you must create the reports yourself. The benefit is that you get exactly what you want.
All of the above are free. AWStats and Webalizer are commonly provided by webhosts, and are also available for download for use on your PC. Google Analytics requires a free registration and the placing of code in your web pages. MySQL is a free database application for Linux, Windows, and other OS.