I want to understand how people are using my product, however privacy is a central tenet of it. How can I implement analytics without having to share users info with 3rd parties (Google etc)?
Mint (<a href="http://haveamint.com/" rel="nofollow">http://haveamint.com/</a>) is a very popular self hosted analytics package. Though depending on how strict your privacy concerns truly are you should still look into google analytics. Google doesn't allow you to store PII according to their Terms of Service. Though they do get various data, much of it would be hard for them to link back to a distinct user. With that said if privacy is still a top concern Mint is a great choice and many people even without the privacy concern are opting for it over google analytics.
You'll need to deploy your own private log analytics. While there are plenty of products developed over the past decade to help you do this, the "in" approach these days is a combination of Hadoop for storage and ETL and a more traditional data warehouse for summary queries and reports. Several presenters[1] at Hadoop World 2010 covered this.<p>1- <a href="http://www.cloudera.com/company/press-center/hadoop-world-nyc/agenda/" rel="nofollow">http://www.cloudera.com/company/press-center/hadoop-world-ny...</a>