No.... you don't get cancer from heating your food in a microwave. There's no '
radiation' (as like in
radioactivity) involved here. A Magnetron produces the microwave power, which in turn cause the water molecules in food to vibrate thus producing heat.
Microwave radiation is
non-ionising, it can only cause molecules in the food to move. But microwave radiation cannot alter the chemical structure of food components.
However, if you are cooking meat then there can be complications. It's said that uneven distribution of the microwaves, and can leave cold spots in the food that harbour dangerous bacteria, such as E. coli, salmonella, listeria and in the case of pork - Trichinella.
Earlier people used to take care with microwave ovens, usually placed above the waistline (protect your male organs from microwaves), but all Microwave ovens are built to a specification - US - 21 CFR 1030.10- which limits the amount of microwaves that can leak from an oven throughout its lifetime to 5 mW of microwave radiation per square centimeter at approximately 2 inches from the oven surface.
This limit is far below the level known to harm people. Microwave energy also decreases dramatically as you move away from the source of radiation. A measurement made 20 inches from an oven would be approximately
1/100th of the value measured at 2 inches from the oven.
So when you operate the microwave, just stay away from it just as a precautionary measure.