We present the largest catalogue to date of optical counterparts for H I radio-selected galaxies, HOPCAT. Of the 4315 H I radio-detected sources from the H I Parkes All Sky Survey (HIPASS) catalogue, we find optical counterparts for 3618 (84 per cent) galaxies. Of these, 1798 (42 per cent) have confirmed optical velocities and 848 (20 per cent) are single matches without confirmed velocities. Some galaxy matches are members of galaxy groups. From these multiple galaxy matches, 714 (16 per cent) have confirmed optical velocities and a further 258 (6 per cent) galaxies are without confirmed velocities. For 481 (11 per cent), multiple galaxies are present but no single optical counterpart can be chosen and 216 (5 per cent) have no obvious optical galaxy present. Most of these 'blank fields' are in crowded fields along the Galactic plane or have high extinctions.Isolated 'dark galaxy' candidates are investigated using an extinction cut of A(Bj) < 1 mag and the blank-fields category. Of the 3692 galaxies with an A(Bj) extinction < 1 mag, only 13 are also blank fields. Of these, 12 are eliminated either with follow-up Parkes observations or are in crowded fields. The remaining one has a low surface brightness optical counterpart. Hence, no isolated optically dark galaxies have been found within the limits of the HIPASS survey.