The evidence for the danger associated with mobile phones is quite sparse as the technology is fairly new and the timelines for potential causal effects quite long. Research does tend to point towards a fairly low risk for effects such as tumours or similar. That hasn't stopped an entire industry building up to promote products said to lessen said risk.
Most phones work on a radio frequency that is similar to Microwave ovens. However, they work at a power output of around 0.7 watts, whereas ovens work at around 700 watts and also have instruments to focus and contain the waves to heat your coffee. To date, several huge studies have been done, on thousands of mobile users and not one has found any real or worrying adverse affect of the radiation emitted from the devices.