Gamma-rays can go through a body but they will ionize a lot of atoms (I don't know whether some of the gamma photons will go through without any interaction at all?). The same for X-rays. Visible light and infrared (till $1mm$) probably only reflects and absorbs. But perhaps rays from 1 cm and longer (radiowaves) can get through the human body without harming the body or without changing in frequency?
There are two effects of electromagnetic waves on human body.
- Heating effects, occurring mostly around 2.45 GHz (which is the frequency used in microwave ovens)
- Ionizing effects, which can damage human body and cells
Here is a picture of how the radiowaves penetrate the human body according to the frequency. The legend is from 1 to 10 : Cosmic rays, gamma rays, X-rays, ultraviolet, visible spectrum, infrared, microwaves, radiowaves, very low frequencies, extremely low frequencies.