Can apps access my camera without telling me?
This question over on StackExchange lead me to Apple's iOS Developer Guide, specifically, the background section. This lists the activities apps are aloud to run in the background, camera access is not one of them. 

This would also be a terrible condition for battery life and so it is not surprising that it is not supported. While this doesn't guarantee that none of your apps will try to get access to your camera, you can rest assured that if anyone tried to, Apple would reject their app. 

This also ensures that there's no API for background camera access, so unless someone has figured out a way to hack non-jail broken iOS at a very low level, we can all sleep safely with only the watchful eye of Siri upon us. 

Edit:
Per my discussion with timothymh below, I realized you may have been asking about if you are still using a given app, having take a picture without switching to a new app. With more interesting reading from Apple's Developer Guide, we find that the camera API won't hand you data until a picture is taken or a video completed. Because the camera isn't handled by a daemon, it would be very difficult to be constantly polling the camera for input, even if you found a way past the API to get data without user input. Note I'm not an Apple developer, but from an official standpoint, it appears what you're talking about shouldn't be possible.