Two types of waves that some people find most interesting are gamma-rays and x-rays. Gamma-rays have a wavelength starting around .03 nanometers and frequency starting around 6.009 x10^10 GHz. These get progressively smaller and bigger, respectively (the size and frequency of the waves). Instances where gamma-rays occur include medical therapy, nuclear reactions, and things in space like supernovas and stars. Gamma-rays have the most energy of any of the waves. It is said that gamma-rays can emit more energy in 10 minutes than our sun can in its entire 10-billion year expected lifespan. Humans cannot see gamma-rays, it takes a special type of telescope to see them.
Second, x-ray waves start at about 3 nm and a frequency of 2.459 x10^7 GHz. They get smaller and bigger, respectively (the size and frequency of the waves), until they reach .00623 nm and 4.809 x10^10 GHz. X-rays are used primarily for medical diagnostics to view bones and other parts of the body. There are classic x-ray machines, but now there are things like CAT Scans and MRI machines which view your body more in depth. Our sun generates mostly x-rays, even though it is visible light, the waves themselves have characteristics of x-rays. High energy particles emitted from planets in our solar system can be seen through certain telescopes because they are hot enough to emit x-rays. The sun's x-rays aren't harmful to us because our atmosphere absorbs most of them. However, the use that most everyone knows about in the world is medical diagnosis because of the energy the x-rays emit that isn't powerful enough to harm us, but it is powerful enough to take images of things under our flesh.
This is the burst of a gamma-ray when a black hole is being created, pictured 12.8 billion light years away from Earth. Obviously if we can see it that far away, the energy must be pretty high. This picture was taken with NASA's Swift satellite in deep space. This object is among the most distant objects ever detected.
This is an x-ray of somebody's neck/spine. The energy transmitted from the x-ray is powerful enough to see inside the body.