Why do low-energy waves produce heat, but high-energy waves do not? Radio waves, microwaves and infrared are known to produce heat and even cause burns, while visible light and ultraviolet are not. This seems counterintuitive to me, as the latter contain the highest amount of energy.
Why is this? Does it have to do with the quantity of waves rather than the energy?
 A: We need to clear something up first, which is the difference between photon energy and energy delivered by an absorbed wave. Photon energy is what you’re referring to in your question, but photon energy has nothing to do with total energy delivered. For example, 1 Watt is pretty bright for a laser, but it’s pathetic for your kitchen microwave.
So why would you use a microwave to heat things rather than a UV laser of the same average power? Low-photon-energy, long-wavelength waves tend to get absorbed a deeper depth into the material. Also, long wavelengths are difficult to pinpoint because of diffraction. So with long wavelengths, you have a large and deep absorption volume, which leads to general warming.
In contrast, short wavelengths can be better focused, and they tend to be absorbed near the surface. So the energy delivered is localized, tending to ablation and burning of the material. It’s still heat, but just delivered differently.
And, of course, everything I’ve written is a gross generalization.
A: The amount of heat generated by an EM radiation source depends on many factors, including how much of it is absorbed by the material.  Of course in the microwave and infrared, absorption is high in liquids and solids and those sources rapidly produce heating by rotational and vibrational excitations being rapidly converted to kinetic energy.  High frequencies can produce heating also, of course, but at the visible and above, the absorption of photons starts to have chemical consequences instead of just rotational/vibrational consequences.  For instances, instead of ultra-violet light producing an excited vibrational state in a molecule, it will cause an electron to be ejected or for a chemical bond to break.  This may be less likely to be translated into kinetic energy in the short term.
Very high frequency radiation can sometimes pass through material, or it will have chemical consequences instead of thermal consequences.  But some high frequency radiation will be converted to thermal energy quickly.  Highly radioactive substances emit gamma radiation and, and if handled (which they never should, of course) are known to cause a heating around them.
A: I'd like to add to the other answers by mentioning that absorbance is a function of photon frequency (thus also the photon energy, through $E = h \nu$). For instance, here's a Wikipedia article on the absorbance of water.
