You can use Google Analytics API part for handling exceptions. It also provides facilities for collecting stack traces. (this is an exmaple from the API pages)
// Using StandardExceptionParser to get an Exception description.
try {
// Request some scores from the network.
ArrayList<Integer> highScores = getHighScoresFromCloud();
} catch (IOException e) {
// Get tracker.
Tracker t = ((AnalyticsSampleApp) getActivity().getApplication()).getTracker(
TrackerName.APP_TRACKER);
t.send(new HitBuilders.ExceptionBuilder()
.setDescription(
new StandardExceptionParser(this, null)
.getDescription(Thread.currentThread().getName(), e))
.setFatal(false)
.build()
);
... // Display alert to user that high scores are currently unavailable.
}
Afterwards all tracked stracktraces will be display in the Google Developer Console in the tap of you app.

You can also add an Listener for catching unhandled exceptions. So whenever an exceptions occours which you did not expect whis handler will be invoked.
Thread.setDefaultUncaughtExceptionHandler(new MyReportHelper());
Of course you should always try to catch and handle all exceptions which you know of, this handler is only for emergencies. For more details how an handler could look like see here.