Then there is non-ionizing radiation, which encompasses the vast majority of light we are exposed to: visible light from lightbulbs, infrared light from an oven and from people, gigahertz light from our wifi, megahertz light to/from our cell phones, and radio waves hitting our car radio. They are not harmful in small doses because one photon does not have enough energy to ionize atoms and/or break apart molecules. In very large doses, non-ionizing radiation can be harmful. For example, a visible light laser with sufficient power (at least several hundred times more than a legal laser pointer) which is concentrated in a small enough spot will burn your skin and do worse things to your eye if it gets in there. And those of us who are old enough, remember the gerbil-in-a-microwave flash animations which went viral 17 years ago  as a humorous (but not exactly factual) representation of what would happen if you microwaved a live rodent.
The energy of electromagnetic radiation is determined by its frequency; ionizing radiation is high frequency, and therefore high energy, whereas non-ionizing radiation is low frequency, and therefore low energy. The NCI fact sheet Electromagnetic Fields and Cancer lists sources of radiofrequency radiation. More information about ionizing radiation can be found on the Radiation page.