Simple models of cell phone radiation
There are two basic ways electromagnetic radiation can transfer energy to a biological system to cause damage: thermal and molecular.
Thermal energy is cooking, heating, sunburns. You need a large amount of energy and it's typically in the range of visible light (in order: radio -- infrared -- visible -- ultraviolet -- x-ray/cosmic ray/nuclear). The peak instantaneous power output from any cell phone is 3.6 watts; the average power output is substantially lower. The capacity of a Lithium-polymer battery is about 300 Watt*hours per liter (Wh/L); a cell phone battery is about 6 milliliters, so the average cell phone battery has a capacity of about 2 Watt*hours. Given that people typically charge their phone once a day and probably talk between 30 minutes and 1 hour per day, plus the constant discharge rate required by the phone to check in with the network on occasion. Let's assume the energy of the talking-for-an-hour and not-talking-for-23-hours demands are roughly equivalent. That is you expend no more than 1 watt on talking, and one watt on being ready to talk. Assuming you plug in your phone before it dies, you're virtually certain the power output during that hour is less than 1 Watt, which agrees with the wikipedia article below. Let's say it's 0.8 watts. More than half of that is radiated away from you. The geometry might be an interesting exercise for solid geometry students. But let's say the flux through your head is 50%, we're now talking 400 mW for one hour, probably broken up into several chunks, but let's assume you just blast your head for one hour straight. And, remember, the intensity decays at a rate proportional to r^2.
Ignoring the attenuation due to scattering induced by hair, molecular cell membranes, proteins, extracellular elements, like your bony skull, etc, we can model the head as a bag of water. That's pretty much the worst case scenario. So what happens to that 400 mW in your bag-of-water head? The real permittivity of liquid water at 25 C to light at 827 MHz is about 78.27 (a unitless number) and the imaginary component of permittivity is about 2.00*, so the absorption coefficient, alpha, is about 7x10^15 Watts per meter. That is, the power attenuation per unit length is 7,000,000,000,000,000 watts per meter. That 400 milliwatts is absorbed by the first few layers of skin and dissipated spherically as black body radiation, just as though you were sitting outside in the sun and your scalp got warm. You expose your brain to more black body radiation taking a 10 minute walk on a sunny day than you do listening to a cell phone.
Now, let's assume your head is a vacuum and that cell phone radiation got clean through many more times flesh than it actually takes (see above paragraph). Molecular damage occurs when a photon is of just the right frequency to snap a bond and happens to run in to just that kind of bond. These interactions are almost universally at wavelengths much much shorter (higher frequency) than thermal radiation. Ultraviolet light, which has wavelengths in the nanometers, about the length of molecular bonds, is famous for this. It actually takes very special biological molecules to capture visible light, which is at 500 to 700 nanometers. Mainly the porphyrin rings in clorophyll and blood. In any case, it is still dose dependent. Cell phones transmit between 824 and 829 Megahertz, roughly in the VHF radio range, rather deep into the radio spectrum, with a wavelength of about a meter. Roughly speaking, you would need a homogenous structure (like metal, salt, or a body of water) at least 0.25 meters in length to expect any interaction. While DNA may be longer than 0.25 meters, it is not stretched out inside a cell: there are no intracellular nuclei that are 0.8 feet long to accomodate such a stretched out piece of DNA.
Here is a fairly good article on the issue if you want stats; if you find the part about mobile phones and cancer, you'll see that in large population samples studied over decades, no evidence of increased risk has been found.
http://en.wikipedia.org/wiki/Mobile_phone_radiation_and_health
*Permittivity values interpolated from CRC Handbook of Chemistry and Physics, 81st Edition, CRC Press, 2000. I just rough-guessed between the published values (freq, real, imaginary): (500MHz, 78.31, 1.90) and (1000GHz, 78.16, 3.79)
