We recently added a "Please rate this app" kind of dialog in OpenDocument Reader. I was not expecting too much, but thought it might be worth a try to get rid of those years-old bad comments. After the update, the number of good ratings (4+ stars) actually increased! I wasn't sure what was causing the sudden rise of good-mood users, but then I remembered that we added the aforementioned dialog which kindly tries to "remember" the user to rate the app if he likes it.
Unfortunately I don't have any real-world data to show, because I really didn't expect such a dramatic change in ratings.
In case you're interested: we went for the Android-RateThisApp library. Of course, implementing such a dialog yourself shouldn't take too long, but this library worked quite well for us so far.