We present the most complete atlas of nuclear rings to date. We include 113 rings found in 107 galaxies, six of which are elliptical galaxies, five are highly inclined disc galaxies, 18 are unbarred disc galaxies and 78 are barred disc galaxies. Star-forming nuclear rings occur in 20 +/- 2 per cent of disc galaxies with types between T = -3 and T = 7. We aim to explore possible relationships between the size and morphology of the rings and various galactic parameters. We also aim to establish whether ultra-compact nuclear rings are a distinct population of nuclear rings or if they are merely the low-end tail of the nuclear ring size distribution. We produce colour index and structure maps, as well as H alpha and Pa alpha continuum-subtracted images from Hubble Space Telescope archival data. We derive ellipticity profiles from H-band Two-Micron All-Sky Survey images in order to detect bars and find their metric parameters. We measure the non-axisymmetric torque parameter, Q(g), and search for correlations between bar and ring metric parameters, and Q(g). Our atlas of nuclear rings includes star-forming and dust rings. Nuclear rings span a range from a few tens of parsecs to a few kiloparsecs in radius. Star-forming nuclear rings can be found in a wide range of morphological types, from S0 to Sd, with a peak in the distribution between Sab and Sb and without strong preference for barred galaxies. The ellipticities of rings found in disc galaxies range from c(r) = 0 to c(r) = 0.4, assuming that nuclear rings lie in the galactic plane. Dust nuclear rings are found in elliptical and S0 galaxies. For barred galaxies, the maximum radius that a nuclear ring can reach is a quarter of the bar radius. We found a nearly random distribution of position angle offsets between nuclear rings and bars. There is some evidence that nuclear ring ellipticity is limited by bar ellipticity. We confirm that the maximum relative size of a star-forming nuclear ring is inversely proportional to the non-axisymmetric torque parameter, Q(g) ('stronger bars host smaller rings') and that the origin of nuclear rings, even the ones in non-barred hosts, is closely linked to the existence of dynamical resonances. Ultra-compact nuclear rings constitute the low-radius portion of the nuclear ring size distribution. We discuss implications for the lifetimes of nuclear rings and for their origin and evolution.