Gamma Ray telescopes - they study high energy gamma rays that originate from supernovae, neutron stars, etc.. They require the use of a high altitude balloon or a space mission, as gamma rays are absorbed by the atmosphere.
Ultraviolet telescopes - as from the name itself, these telescopes make their observations at ultraviolet wavelengths. These also require a high altitude observation.
X-ray telescopes - measure x-rays. They can only be observed at the high level of the atmosphere or at space, as x-rays can never travel distances through the atmosphere.
Hope this helps.