How can I listen to free radio on an iPhone? Is it possible to listen to the radio for free on the iPhone? 

Do I need a special app? 

I have downloaded some apps for digital radio that require payment, but I just want to listen to regular free radio
If you're referring to normal, terrestrial radio such as you'd get in your car or a cheap clock radio, the answer is that you cannot. At least, not without buying a receiver, something like this Griffin radio receiver.