We investigate the neutral hydrogen (HI) content of sixteen groups for which we have multi-wavelength data including X-ray observations. Wide-field imaging of the groups was obtained with the 20-cm multibeam system on the 64-m Parkes telescope. We have detected ten previously uncatalogued HI sources, one of which has no visible optical counterpart. We examine the HI properties of the groups, compared to their X-ray characteristics, finding that those groups with a higher X-ray temperature and luminosity contain less HI per galaxy. The HI content of a group depends on its morphological make-up, with those groups dominated by early-type galaxies containing the least total HI. We determined the expected HI for the spiral galaxies in the groups, and found that a number of the galaxies were HI deficient. The HI deficient spirals were found both in groups with and without a hot intra-group medium. The HI deficient galaxies were not necessarily found at the centre of the groups, however, we did find that two thirds of HI deficient galaxies were found within about 1 Mpc from the group centre, indicating that the group environment is affecting the gas-loss from these galaxies. We determined the HI mass function for a composite sample of 15 groups, and found that it is significantly flatter than the field HI mass function. We also find a lack of high HI-mass galaxies in groups. One possible cause of this effect is the tidal stripping of HI gas from spiral galaxies as they are pre-processed in groups.