Last week I released AnkiDroid 0.5.1, and judging by the Android Market's comments, people seem to love it :-)
Since a few releases already, an opt-in feedback mechanism sends us a report everytime a problem happens. The anonymous reports are automatically scanned by a Google App Engine application to determine whether it is a new bug or just an additional occurrence of an already known bug. The data can be exploited in two ways:
1) An online application allows one to browse the reports and bugs, see which bugs happen the most often for a given version, and associate them with issues in the bug tracker.
2) A set of Business Intelligence tools allows one to drill-down reports in a multidimensional OLAP cube, and generate reports to show any interesting findings. As a quick example, here is the distribution of crashes among Android versions. Those tools use the open source Pentaho Business Intelligence suite.