I don't think so, Nick.
Fairly sure I was told by a professor/doctor at some point that it was very unlikely that phones can give you cancer. It was probably by the person that taught us cancer, now I think about it.
Though it is early days and knowing the effects are hard to determine and will take years to know, but I'm on the 'stop fear mongering' bandwagon.
...if you call 20 years of studies 'early days' I guess.
I have found that if you say the word 'radiation', people get all excited, and they believe the world is coming to an end. I can only put this down to the media's use of the word with regard to nuclear fuel/power stations/bombs etc, when really they mean 'radioactivity'. There is no logic to it. There is no place in the universe you can go without being radiated by something, and those 'somethings' (x-rays/cosmic rays/gamma rays etc) are probably making you age or worse.
That's not to say it's safe to sit in a microwave oven. Those microwaves, although fairly harmless, are intense enough to heat stuff up in the confines of the oven. So you may not get damaged cell-wise or dna-wise, but your gonna get cooked. And the oven needs some shielding around it because otherwise you're gonna get interference on phones, alarm systems etc around the neighbourhood.
Transmissions from cell phones are in the same band or even lower band 400Mhz to 1.4Ghz. This is a very safe range, and is needed so that you can connect to a cell tower up to 5km away. Your portable phone, wireless internet router/printer etc operate at even higher Ghz, which is why their range is so weak. No-one seems to complain about those cooking your brain or other bits.
