Unfortunately I don’t use an iOS device so I can’t talk about the different apps that are available for iPhones/iPads so if you know of them, please post a small review in the comments. For Android devices there are at least 10 apps available at the time of this writing. I am only going to mention a couple of these as some of the paid versions don’t seem compelling enough to recommend that you shell out money for them when perfectly good free apps are available.
ARDrone Flight by MeavyDev (Market Link) Free
ARDrone Flight is my personal favorite for two reasons. First off, it allows you to record the video from either camera or even both at the same time. Secondly, I can change the tilt control to be an on-screen joystick just like the altitude/rotate controller.
There are a few others that are looking promising and other free apps that have really bad reviews. If you are just starting out, I suggest starting with one or both of these here.
If you are an iOS user, please post some good apps in the comments.