Stats & audience appraisal opensource solutions to install yourself

Check out phpmyvisites or awstats (CGI script). Both use a database and provide you with a javascript tracker to insert into your pages, and an interface to observe and analyse the harvested results.

Freely available, externalized stats / audience measurment solutions

Similarly xiti (look for 'xiti free') or google analytics propose the same javascript tracker thing, yet they hold the database. There is a web interface to configure the observed sites and javascript to gather information about the visitors (screen resolution, available plugins, geolocation of visitors, biggest entrance / exit pages etc...).

Of course you also have costful solutions... :)