The UK government has been studying the same question for the past 11 years. Its Mobile Telecommunications and Health Research (MTHR) study concluded there was no connection at all between cellphones and cancer, and has closed down the research unit.
As MTHR's chairman said: "This independent programme is complete, and despite exhaustive research, we have found no evidence of risks to health from the radio waves produced by mobile phones or their base stations. Thanks to the research conducted within the programme, we can now be much more confident about the safety of modern telecommunications systems."
Which should reassure those of us who use cellphones regularly or whose children will grow up in a world where cellular communication is the norm.
So why were we so concerned in the first place? I think it's the term "radiation" and those connotations of death rays, microwaves, x-rays and the like. The word conjures up images of creeping death, of nuclear devastation, of The Hulk rampaging across a benign world. It's scary and, in this case, quite misleading.
A better word for how cellphones operate is "radio". That's all it is. It's a radio, much like a walkie-talkie or the alarm clock radio beside your bed or the one in your car. It sends and receives radio waves and that's something we've been studying for nearly 100 years, since the radio was first invented.
In that time, the incidence of brain tumours and cancers has remained flat. Surely we would have seen some kind of increase, some kind of relationship between the two if radios caused cancer?
During that 100 years, we've also seen television burst on to the scene. Television also uses radio waves to transmit the signal, yet even with both radio and television in our homes the incidence of brain cancers and tumours remains flat.
The past 10 years have seen the use of cellphones skyrocket. No longer a yuppie toy, now it seems everyone has one. The incidence of brain cancers and tumours must surely have moved, given how close to our heads we hold these things? But no, there is no variation - brain cancers and tumour rates remain flat, unaffected by the increase in usage.
Today, roughly five billion people around the world use cellphones. Surely, if there were any link at all between cellphones and cancer, we would have seen a rise in the incidence of such things, but we haven't.
For a long time I was happy to say research should continue because we just don't know enough, but now I think we do. We know that despite thousands of studies, millions of hours of use and billions of users all holding these radios up to the sides of their heads, the incidence of brain tumours has not risen.
It's time to put these worries aside. There are plenty of things that are out there to occupy our researchers and I'd rather they were studying those than trying to find a link that isn't there.
If you want to know more about how cellphones work, I recommend the www.emfexplained.info website.
Paul Brislen is chief executive of the Telecommunications Users Association of New Zealand.