I have several free (no ads either) apps in the Android market, and even in the most trivial of apps I will include Google Analytics to receive crash reports, see what screens are most popular (so I can improve my apps where it matters most), where the app is being used (for some reason one of my apps was really popular in France, I then added a French translation and the adoption really took off), what devices are most/least popular etc. If I add a new feature, I want to know if its being used or if I wasted my time, if I need to improve the discoverability of the feature etc.
Last but not least, the usage data is really motivating to me as a developer of free apps. If I release an app, and I see it being used daily, that makes me happy and motives me to keep updating it.
As far as I know, the GA data is anonymous and only shown to the developer in aggregates.