The greater the frequency range of a transmission medium, the greater the number of bits per second it can transmit. In other words, the bigger the bandwidth in hertz available, the bigger the bandwidth in bits per second that can be transmitted.
Given that, why we don't use gamma rays, x-rays or ultraviolet to transmit data instead of e.g. visible(light) in optical fiber or microwaves(cell phones)?
For data transmission through optical fibers, what you have to worry about is finding the correct material for transmitting the light over long distances. Consider the following diagram for the attenuation through an optical fiber (from NASA through wikipedia):
You can see that there is a minimum in the losses through the fiber in the IR because both the scattering of light in the fiber and the absorption of light through the fiber are at a minimum here. Since we'd like to transmit information with the least amount of power, this will dictate our choice of radiation energy (wavelength) for fiber optics.
For free space transmission, it wouldn't be good to use "high" energy radiation such as gamma rays and x-rays because they could be dangerous for peoples health. Also, the air can scatter high energy radiation (we see a blue sky because of this scattering of blue and violet light for instance).
Actually, NASA and others are considering the use of X-rays as a communication medium. The difficulty comes in the modulation, and in the fact that X-rays can't be transmitted via wires or fiber. But for vehicles re-entering Earth's atmosphere, X-rays provide a benefit in that they aren't stopped by the ionizing effects of re-entry. X-rays are also more difficult to focus than visible light. Even though the energy is carried in photons, the higher energy photons don't react in the same way to optical elements. Lastly, as ionizing radiation, X-rays and gamma rays do have potential health consequences associated with exposure, so any use of these must take into account the safety of those using them, as well as by-standers.
for "wired" transport, you need efficient and compact way to produce, receive, repeat the signal, but also materials able to conduct the given frequency, and materials able to manipulates it (mirrors, lenses...) with the expected effect, with little absorption, and without aging under the energy.
for direct transmission through air you need frequency windows where air is really transparent (real air, including vapor, etc). In addition you can have constraints about the size of the antenna and direct visibility (lower frequencies like sound and radio-waves can a bit turn around obstacle, goes into tunnel and walls. "light" cannot.).
High frequency data transmission is not as practical with limited applications. Range decreasing as frequency increases. Data transmission can use phase modulation to pack more data in narrow bandwidth. This gets harder to do as frequency increases.
