While this would not work for many people... I log most stuff to a database. I have an admin panel where admin people can perform simple extracts. The extracts can then be crunched by analysts in any way they want. We don't have millions of users, as we are B2B, but it lets the sales guys load the data into an excel template that does what they want. Then they can focus on what people are using and what they should pitch towards. This would probably be a terrible solution for high user apps, but it has worked great for high value low user stuff that I usually deal with.

https://github.com/snowplow/snowplow <disclaimer: co-founder>

I second SnowPlow; the difference between them and other offerings (like Piwik) is that they don't attempt to be a Google Analytics knockoff, but have a distinct philosophy about how analytics should function.

And there is a library for Arduino!

SnowPlow is the best.

SnowPlow + Looker is a really powerful and flexible combination. [Disclaimer: I work at Looker.]

http://newrelic.com/ has analytics for web client, mobile client and server side.

Looking at their mobile offering, I would love for Amazon to move into the space. I am curious to know what are you lacking right now in GA that you're looking for another free solution?