One example that I know of and use daily is the ability to reset the missed call notification counter. I have Go Dialer, which is a replacement for the stock dialer and contact app (how you make phone calls). When I miss a call, android lets me know that with a notification. However, Go Dialer is not allowed to reset this counter, even though it asks for that permission when you install the app. Android 2.2 and earlier let user apps reset it, but made this permission a system-only accessible permission for android 2.3