Free tool to analyze web server logs
Web servers log a lot of information regarding request served. These logs can be used extract a lot of information about your site. For example which images are requested most, which pages are famous etc etc. As these logs are in text format so its very difficult to get any meaningful information manually.
I have recently used a tool to get a lot of information which helped in performance optimization of my site. The tool is called WebLog Expert. The tool can analyze apache or iis logs both in compressed form (gzip) or plain text format. Its Lite version is free of cost but pro and std version have small tag price. More information can be found at weblogexpert.com.