The endless analytical opportunities from it being open-source.

I like to own the data I manage. Most free analytics solutions don't offer that. With Piwik you host your data analytics on your own server, not sharing it with third-party services (like ads). I like some features of Piwik too (like Piwik Overlay Maps which show how many clicks each on-page link has triggered). It's a nice visualization of how users interact with my pages. Other reports are probably standard: You get to see top referrals, top referral keywords (most will be non-provided), conversions / goals, landing / entry and exit pages and so on. If you get a lot of traffic, you'll find real-time map feature very addictive too. The dashboard view is very easy to customize which I loved

Its opensource and you can develop it, piwik has a good community. Piwik is a great alternative to Google Analytics if you need something to run on your own servers. It also helps to analyze traffic more closely by turning on features to track ip addresses. This allows for closer analysis of activity on your website.