When to unregister BroadcastReceiver? In onPause(), onDestroy(), or onStop()?

it depends on where you have register the receiver. The complementary method pairs are

onCreate - onDestroyonResume - onPauseonStart  - onStop

if you register the receiver in the first one then unregister it in it's ending method.

From the Android documentation:

You should implement onStop() to release activity resources such as a network connection or to unregister broadcast receivers.

Then, I would follow these pairs (using @StinePike's analogy):

onResume - onPauseonStart  - onStop

Because of the Android Lifecycle, and as @w3bshark mentioned:

In post-HoneyComb (3.0+) devices, onStop() is the last guaranteed handler.

It is just as simple as that, if you want to listen for events even when your activity is not visible then call unregister in onStop()(E.g From Activity A you open Activity B but if you want A to still listening for the events).

But when you only want to listen only for events when your activity is visible then in onPause call unregister() (E.g From Activity A you opened Activity B but now you do not want to listen for events in activity A).

Hope this helps your problem.