What types of electromagnetic waves can be described as ionising?

High energy UV, X-rays and gamma rays.

Edit to dx: The hydrogen ionisation energy you quoted falls in the extreme/vacuum UV range. As I said ...

Depends entirely on the atom you're concerned about. Each atom has a different energy at which it becomes ionised, due to varying numbers of protons and electrons. If you take Hydrogen as an example, its ionisation energy is 13.6eV which corresponds to an electromagnetic wavelength of 91.18 nm.

This can be calculated by converting eV to Joules (by multiplying by 1.6*10^-19) then using the equation E=hf (where h is Planck's constant and f is the frequency of the electromagnetic radiation) and the fact c=wavelength*f (where c is the speed of light).

I think all em wave shave potental tp ionose it more depends upon the medium and its dielectric strength.