Radiation, even in small doses, can cause cancer in humans and other living things. Fast moving photons (gamma rays), electrons (beta rays) and helium nuclei (alpha particles) can crash into other molecules and change their structure. If this happens to a DNA molecule, it can damage the genetic information, and sometimes turn a cell cancerous. Radiation also causes burns, much like sunburn, in large doses over short amounts of time.
Radioactive iodine is also readily absorbed by the body and becomes incorporated in bones, and is therefore difficult to eliminate from the body. The radiation it emits can cause bone cancer over long periods of time.Source
How much radiation is too much radiation? See the answer here.