Depends on what waves you mean. Waves are a movement, basically. Water comes in waves, light comes in waves, radio comes in waves. The microwave also.
Water-waves can crush ppl obviously if they are strong & big enough. So that's probably not what you meant.
Light changes color when the wave-length changes. Blue light has short wave-lengths red light has long wave-lengths. Intense short wave light (ultraviolet) can cause sunburn.
Radio waves are everywhere since last century. Mobile phones, Radio, satellites... everyone uses radio. There are sometimes strong magnetic/ electric fields very close to radio towers or beneath high voltage power lines. It is yet discussed whether these may damage people, because the nerves inside the human body may be irritated by those fields. Some people claim to be sensitive to this "electromagnetic pollution". They get headaches or other symptoms. Yet it is unknown whether this is really caused by the electric fields or whether it's a placebo-effect because people believe that these will be affected by such fields. There were also studies about people getting cancer in the places where they carried the mobile phone antenna. But I'm not sure whether they found that mobiles are a relevant cause of cancer or whether it was just by chance that the tumor was behind the ear in a couple of patients.
Microwaves obviously can do damage to living things, because they heat water inside any object. Also inside living things.
Wave power is the transport of energy by ocean surface waves, and the capture of that energy to do useful work — for example, electricity generation, water desalination, or the pumping of water (into reservoirs). Machinery able to exploit wave power is generally known as a wave energy converter (WEC). Wave power is distinct from the diurnal flux of tidal power and the steady gyre of ocean currents. Wave power generation is not currently a widely employed commercial technology although there have been attempts at using it since at least 1890. In 2008, the first experimental wave farm was opened in Portugal, at the Aguçadoura Wave Park