There are a lot of Web log analysis tools out there, and many are free. This is a list of some of the best free log analysis and Web analytics tools available.
Deep Log Analyzer is the best free Web analytics software I've found. It is a local log analysis tool that works on your site logs without requiring any codes or bugs on your site. It's not as fancy as Google Analytics, but it does offer a few extra features. Plus, if you need more features, there is a paid version you can upgrade to.
Google Analytics is one of the best free Web log analysis tools available. There are a few reports that are not included, but the graphs and well-defined reports make it very nice. Some people don't like giving a large corporation like Google such direct access to their site metrics. And other people don't like needing a bug placed on the Web pages in order to track them.
AWStats is a free Web analysis tool that works as a CGI script on your Web server or from the command line. You run it and it evaluates your Web logs with many different reports. You can also use it to analyze FTP and mail logs as well as Web log files. Some useful features include the ability to export reports to XML, text, and PDF, a report on 404 pages and the referrers for them, plus all the standard visitor and pageview stats.
W3Perl is a CGI based free Web analytics tool. It offers the ability to use a page bug to track page data without looking at log files or the ability to read the log files and report across them.
Power Phlogger is a free Web analytics tool that you can offer to other users on your site. This tool uses PHP to track information. But it can be slow.
BBClone is a PHP based Web analytics tool or Web counter for your Web page. It provides information about the last visitors to your site tracking things like: IP address, OS, browser, referring URL and more.
Visitors is a command line free log analysis tool. It can generate both HTML and text reports by simply running the tool over your log file. One interesting feature is the real time streaming data you can set up.
Webalizer is a nice little free Web log analysis tool that is easily ported to many different systems. It comes with several different languages for reports and a bunch of stats to report on.
Analog is a widely used free Web log analysis tool. It works on any Web server and is fairly easy to install and run if you understand how your server is administered. It has a lot of good reports and with another cool can be made even prettier.
RealTracker uses a code that is placed on your Web pages to track your pages, similar to Google Analytics. It offers a bunch of different reports but the real benefit to this tool is that it's easy to add to your pages and easy to read the results. And if you need more features, you can upgrade to the professional or enterprise versions.