By background, I mean none of the application\'s activities are currently visible to the user?
To piggyback on what CommonsWare and Key have said, you could perhaps extend the Application class and have all of your activities call that on their onPause/onResume methods. This would allow you to know which Activity(ies) are visible, but this could probably be handled better.
Can you elaborate on what you have in mind exactly? When you say running in the background do you mean simply having your application still in memory even though it is not currently on screen? Have you looked into using Services as a more persistent way to manage your app when it is not in focus?