Hint about how to create statistics

We need a tool to create access log analyzis or some other way to create detailed statistics like counters for unique visitors, referers , search engines used and what words for search for. We also want to know about the visitors web browsers and what spiders or robots that visited a site.

I know that this is not core business for anyone involved in jahia development but I am sure the question usually comes up quite frequently.

Of course I am looking for an open source alternative but it is also interesting to know about commercial alternatives that is affordable and/or have good useability or have all the features.

It is also interesting to find out if this could be a built in feature in Jahia?

Currently we have a site which generates the statistics by buying this service from a third party. We include small java script snippets in the jahia templates which call an external site.

Regards

/Lars Hagrot