Microwave ovens aren't natural!
Neither are using computers, living in buildings or wearing clothes. If you want to live in a cave naked, go ahead.
Radio waves were indeed first discovered in experiments by German physicist Heinrich Hertz, based upon James Clerk Maxwell's electromagnetic theory of light. But Hertz died decades before the Nazis came to power and worse yet, after they did, tributes to Hertz for his scientific discovery were purged from public view because of his Jewish heritage.
Claims about the Nazis inventing microwave ovens are contradictory and without evidence. Some claims purport that large microwave ovens called "Radiomissor" had been used by the Wehrmacht during Operation Barbarossa, the German invasion of Russia in 1941. Which of course conveniently ignores the fact that Russia's electricity grid at that time was very sparse, and the Wehrmacht due to its rapid advances already faced great difficulty supplying tanks with fuel, so running electricity generators for the sake of powering microwave ovens seems rather impractical, when horse-drawn field kitchens were widely available and the acquisition of firewood trivial.
In contradiction, other claims state the microwave oven was researched by Nazi scientists for the use outlined above, but cancelled because it was allegedly found that microwave oven food caused cancer (see points below). This again ignores the historical fact that the far more useful military application of microwaves lay in radar, which was still new technology at the outset of World War Two and it therefore would have been unreasonable to direct such research to the purpose of food preparation. It was in fact Percy Spencer, a leading researcher of American radar technology, who would invent the microwave oven shortly after the war and its development by the Raytheon company is well documented. 
Last but not least, if there was a moral imperative that we shouldn't use things the Nazis invented, we would also have to stop driving cars on highways, flying around in jet planes, depending on satellites shot into space with rockets, etc.
 Did James Lovelock really invent the microwave oven?
Dr. Lovelock does claim this on his website and certainly did it before it was commercial and widely available. However the microwave oven was patented in 1945; the earliest claim Dr. Lovelock made was in a 1955 journal article on the reanimation of cryonic preserved rats using microwave diathermy. 
 Why did the Soviet Union ban microwave ovens in 1976?
This is a widely purported myth, but there is no evidence it ever happened. The ban was supposedly based on Soviet research linking cancer growth to food cooked in microwave ovens, but no trace of any such research exists either. 
Heat of any kind can destroy a few vitamins and other nutrients in food. Boiling in water can also remove nutrients, because the nutrients migrate out of the food and into the water, which is thrown away. Since microwave cooking usually involves shorter cooking times and less boiling than conventional cooking methods, it actually destroys fewer nutrients than conventional cooking overall. This doesn't mean either cooking method is "bad for you," though -- you probably get enough essential nutrients from other sources anyway, without having to drag raw foodism into it.
No more so than heating food in a conventional oven does. Yes, a few of the trace compounds created in baking are carcinogenic when ingested in sufficient quantities. But the quantities of carcinogens created by heating food -- in a microwave or otherwise -- are well, well below the threshold where they can have any impact on your chance of getting cancer. Unless you heat it so much that it turns into a lump of charcoal, in which case you'll want to spit it out the moment you taste it anyway.
Nearly all chemical transformations in microwaved food occur because the food simply gets hot. Just like it does in a conventional oven.
This is absolutely true. So does a light bulb. The microwaves generated inside a microwave oven are radio waves with wavelengths from a millimetre to a metre, which carry far less energy per photon than even ordinary visible light. (Gamma rays, by contrast, have wavelengths down to 10-12m, short enough to cause tissue damage by ionization.) The reason microwave ovens are enclosed in wire mesh Faraday cages is because of the amount of microwave radiation, not anything inherently more dangerous about microwaves vs. any other kind of radiation.
Radiation leakage was a concern at one point, but the only way for a microwave oven to leak radiation is if there's a hole in its Faraday cage. And even if there is a hole in the microwave oven, the leaked radiation won't get very far -- within a foot or two, it will have spread out so thin that it won't be any more harmful than the radiation from a cell phone. (Cell phone phobia is another matter entirely....)
There is one kind of radiation microwave ovens freely emit into the environment: thermal infrared radiation. This is because they are at room temperature, and all objects at room temperature emit thermal infrared radiation. (Scary note: Your microwave oven emits thermal infrared even when it's unplugged!)
 Microwave ovens make food radioactive!
No, they don't.
Although many people refer to microwave cooking as "nuking" a piece of food, no nuclear processes are involved or induced. About the only way to make a non-radioactive item radioactive is to bombard it with slow neutrons. While nuclear reactor cores do emit neutrons, microwave ovens most emphatically do not.
 Microwave ovens cook from the inside out.
Not exactly. The microwave field penetrates a certain distance into food and no further; in meats this is about two inches/5cm. Further cooking is done by heat generated from microwaving the outer parts of the food migrating inward.
 They use microwaves at water's resonant frequency
This claim is repeated by a lot of folks, including some physics professors who should know better.
The claim is that microwave heating penetrates into the food, rather than just heating the outside surface, because the microwaves used by these ovens are tuned to exactly the resonant frequency of water molecules. Therefore their energy is absorbed by the water in the food, and bypasses everything else.
Anyone who's ever put a ceramic plate in a microwave oven and had it come out piping hot can tell you this isn't the case. Water molecules have a resonant frequency of around 10 GHz; microwave ovens produce radiation at 2.45 GHz, which is nowhere near this frequency. They do this to allow the radiation to penetrate into the food. If it was at the resonant frequency of water, the water on the surface of the food would absorb all the energy and the heating would have practically zero penetrating power.
It is true, though, that wet food absorbs the microwave energy faster than dry food, due to the fact that microwave radiation preferentially excites polar molecules (such as water and some polar fats). To avoid uneven heating or to speed up heating, you could try to spread water on your food -- the microwave will dry your food anyways, so that will get offset as well.
 Microwaved water is bad for plants
This claim pops up from time to time: Water that's been boiled in a microwave, and then cooled, is somehow worse for your plants than water that hasn't been microwaved, or water that was boiled on a conventional stove.
Mythbusters did a segment about this, with 4 groups of plants: Plants given straight tap water, plants given tap water boiled in a microwave and cooled, plants given tap water boiled on the stove and cooled, and plants given no water. The result: All plants grew about equally well, except for the plants which were given no water, which all died.
 You can't brown a cake or pie in them
Actually, this one's true :(
- Does microwaving food remove its nutritional value? -- from cnn.com (The short answer: No, but make sure you only use microwave-safe cookware.)
- Anything new on the dangers of microwave ovens?, from The Straight Dope 28-Feb-2014
- Cooking in The Microwave Oven: Is It Safe?, a suprisingly well-informed article for a website with "wellness" in its name
- ↑ "Microwave Ovens: The Curse of Convenience"
- ↑ Microwaves, Nazis, Cults, John F Kennedy, Anti-Semites and Christian Fundamentalists — Or cooking a dinner in 3 minutes flat
- ↑ http://www.smecc.org/microwave_oven.htm
- ↑ Andjus, R.K. and Lovelock, J.E. 1955. Reanimation of rats from body temperatures between 0 and 1 C by microwave diathermy. J. Physiol
- ↑ For example: Why Did the Russians Ban an Appliance Found in 90% of American Homes?
- ↑ Microwave Myths (pdf)
- ↑ The Claim: Microwave Ovens Kill Nutrients in Food, New York Times, 17-Oct-2006
- ↑ The Hidden Hazards of Microwave Cooking, at health-science.com
- ↑ Kappe et al., Microwave Effects in Organic Synthesis-Myth or Reality?, Angewandte Chemie, vol. 52 no. 4 (21-Jan-2013), pp. 1088-1094.
- ↑ 10.0 10.1 Radiation, irradiation and our food supply
- ↑ 11.0 11.1 Do microwave ovens cook from the inside out?, on The Straight Dope, 4-Sept-2003