The statistics of strongly lensed arcs in samples of galaxy clusters provide information on cluster structure that is complementary to that from individual clusters. However, samples of clusters that have been analysed to date have been either small, heterogeneous or observed with limited angular resolution. We measure the lensed-arc statistics of 97 clusters imaged at high angular resolution with the Hubble Space Telescope, identifying lensed arcs using two automated arc-detection algorithms. The sample includes similar numbers of X-ray-selected [MAssive Cluster Survey (MACS)] and optically selected [Red-Sequence Cluster Survey (RCS)] clusters, and spans cluster redshifts in the range 0.2<z<1. We compile a catalogue of 42 arcs in the X-ray-selected subsample and seven arcs in the optical subsample. All but five of these arcs are reported here for the first time.