[mikeash]

Yes, apps can definitely listen while in the background. In fact, this is one of the few activities where Apple allows you to run in the background indefinitely. Without doing this or one of the other things (like continuous GPS updates), you only get three minutes of background activity before the OS freezes or kills your app.

Some apps actually use this to work around background activity restrictions. If they can come up with a plausible excuse to run the microphone, they can use that to keep the app active in the background indefinitely.

It does place a really obvious red bar at the top of the screen, though, so it's not something an app can do secretly. I believe only one app can do it at a time, too, so you can't have a bunch of them all spying on you at once.