geeze .... it's a matter of frequency (Hz) + power (W) + distance + duration of exposure ... this is well documented (IEEE) and regulated (FCC/OSHA - and I don't know who else).
Nuclear radiation is ionizing and will directly cause cellular DNA mutation and cause cancer within a few hours ... this is radiation from things like x-rays, gamma rays, etc. The exposure to this type of radiation is measured in rads, if I remember correctly.
Non-Ionizing radiation is from things below the atomic level - things like sunlight, tanning beds, and electromagnetic waves from radio, TV, radar, microwave ovens, electric power lines, cell phones etc. Depending on the exposure - it can cause cell damage which may lead to cancer or other problems. But, it doesn't cause the cell mutation in the same way as ionizing radiation.
To address Corey's concern about microwave radiation and cataracts - yes, it can happen. A friend of Dad's who was inspecting a radar installation one day went blind (from cataracts) within about a week ... some idiot turned the radar on while Willard was standing right in front of the dish.
Will using a microwave oven give you cataracts? Probably not - unless it is damaged and you stand with your face pressed up next to the door during the entire cooking period - and then probably only with multiple exposures.
There was also a concern some years ago for people with pacemakers and microwave ovens. Of course, there was also a potential problem with these same people using power tools. External electromagnetic fields could upset "electronics" in the pacemaker - either shutting it off or altering it's rate. Of course, these pacemakers were generally made of an expoy-resin ... and not shielded from EMR. Since "nuclear powered" pacemakers (Lithium batteries) which are shielded in metal are now common - it's not such a big deal.
I have to deal with this stuff as an Amateur Radio Operator all the time - trust me ... every time I want to play with a new antenna design, or change my power output, I have to go through a lot of calculations to make sure I am in compliance. There are equations, formulas, tables and forms.
Other supposed EMR sources of cancer, or other health problems, are living near high-tension power lines (mental retardation is some children), sleeping under an electric blanket (some cancers and infertility in some men), and using cell phones (brain cancer). There is no conclusive definitive scientific proof of any of these claims.