Microwave ovens allow a maximum leak amount of only 5mW, which is really small1.
If more radiation were let out, you would experience microwave burns2.
Microwave radiation is non-ionizing. Differently from x-rays and gamma rays, the microwave photons simply do not have enough energy to cause cancer through ionization3.
Given the previous well-known facts:
- If you are not burned, you are not being affected by microwaves because they don't leak out.
- If you were to get burned, you would still have no ionizing radiation impact.
Finally, research shows that microwave-length radiation does not cause cancer, but the studies relate mostly to different kinds of microwaves (for example the waves emitted by a cell phone)4.
References:
1: http://en.wikipedia.org/wiki/Microwave_oven#Direct_microwave_exposure
2: http://en.wikipedia.org/wiki/Microwave_burn
3: http://en.wikipedia.org/wiki/Ionizing_radiation
4: http://www.ncbi.nlm.nih.gov/pubmed/21084892