Not all radiation is harmful, and whether or not it is harmful depends on the type of radiation in question and how much (the so-called 'dose') you are exposed to.
Some types of radiation are known as 'ionising'. Ionising radiation includes both electromagnetic sources, such as X-rays and gamma rays, and particles, such as alpha and beta particles. Naturally occurring radon gas, for example, emits alpha particles. Ionising radiation can cause burns, radiation sickness, and cancer.
Some types of non-ionising radiation can also be harmful. For example, using a sunbed or staying out in the sun too long will expose you to ultraviolet radiation, which can cause premature ageing, cataracts and skin cancer.
Other types of non-ionising radiation, such as lasers, can cause burns and eye damage.