In our environment we are subject to many different kinds of radiation from the Electromagnetic Spectrum. When we consider the type of radiation that causes cell damage, and potentially cancer, we look at the higher frequency radiations, basically from ultra violet light up, that cause ionisation of atoms or molecules. There has been some discussion about whether non-ionising radiation, such as radio waves, may also cause damage. One article on the subject is accessible here http://www.cancer.gov/cancertopics/factsheet/Risk/cellphones
Effect of Radiation on Humans
While our environment has a certain background level of iodising radiation that we have adapted to live with, exposure to higher levels of ionising radiation is dangerous.The picture shows burns from high energy Xrays.