As Mr. A. so eloquently put it, this would only matter if the type of radiation was harmful to humans. EM radiation from mobile phones falls in the same bucket as radiation from light bulbs. So where are all the studies on light bulbs causing cancer? There aren't any, because light from light bulbs doesn't cause cancer.
EM radiation can heat up flesh, which is why microwaves work to heat those delicious leftovers. However, there should be some math done here. As an example, I just looked at my own cell phone - it has a battery rated at 950mAh / 3.6Wh. Okay, so if the battery lasts for 1 hour, the phone is heating for 3.6W. My phone lasts for at least two hours talking, though, so then it's heating 1.8W per hour. And that's assuming all the power is going to sending and thus heating. Compare that to microwaves that heat 700W-1100W, which we consider safe.