Microwave ovens give off radiation, but their radiation is different than the type of radiation than causes radiation poisoning and cancer. Microwaves can heat human tissue, however, so proper safety is important.
Microwave radiation is mostly used for cooking because it is easy to create and contain. Microwave radiation heats up water molecules and other parts of food, and it is reflected by metal. In addition, microwave radiation is relatively safe even if a system leaks.
However, microwaves do heat human tissue, and exposure to radiation can lead to damage. The effects of microwave radiation are readily apparent, unlike other types of radiation, and people notice heating before dangerous burns can develop.