The answer is no as the electro magnetic radiation waves break down the molecules in the food to cook it quicker. They don't affect what you are eating and it is a myth.
There is a problem if you use plastic containers to cook the food in though and it is true that you can get cancer from this. In plastics there is a harmful chemical called BPA which has been in use since the 1960's.
Plastic leaking into the food can create a few side effects like increased estroogen in the body which creates issues such as weight gain,hair loss, trouble sleeping and increased PMS. High estrogen can increase the likelihood of breast cancer.
The microwave is not the problem it is what the food is packed in.