The Raman spectrum of hydrogen clathrate hydrates has been measured, as a function of temperature, down to 20 K. Rotational bands of H(2) and HD, trapped into the small cages of simple (H(2)O-H(2)) and binary (H(2)O-THF-H(2)) hydrates, have been analyzed and the fivefold degeneracy of the molecular J=2 rotational level has been discussed in the light of the available theoretical calculations. The vibrational frequencies of H(2) molecules encapsulated in the large cages of simple hydrates turn out to be well separated from those pertaining to the small cages. Comparison with the equivalent D(2) spectra allowed us to assign the large cavity vibrational frequencies to three couples of Q(1)(1)-Q(1)(0) H(2) vibrational modes. Populations of ortho and para species have been measured as a function of time from rotational spectra and the rate of ortho-para conversion has been estimated for both simple and binary hydrates. We suggest, using the H(2) vibrational spectra, a model to analyze the cage population in simple hydrates.