We present a catalogue of photometric and structural properties of 228 nuclear star clusters (NSCs) in nearby late-type disc galaxies. These new measurements are derived from a homogeneous analysis of all suitable Wide Field Planetary Camera 2 (WFPC2) images in the Hubble Space Telescope (HST) archive. The luminosity and size of each NSC are derived from an iterative point spread function (PSF) fitting technique, which adapts the fitting area to the effective radius (r_eff_) of the NSC and uses a WFPC2-specific PSF model tailored to the position of each NSC on the detector. The luminosities of NSCs are <=10^8^L_V,{sun}_, and their integrated optical colours suggest a wide spread in age. We confirm that most NSCs have sizes similar to globular clusters (GCs), but find that the largest and brightest NSCs occupy the regime between ultra-compact dwarf (UCD) and the nuclei of early-type galaxies in the size-luminosity plane. The overlap in size, mass, and colour between the different incarnations of compact stellar systems provides a support for the notion that at least some UCDs and the most massive Galactic GCs may be remnant nuclei of disrupted disc galaxies. We find tentative evidence for the NSCs' r_eff_ to be smaller when measured in bluer filters and discuss possible implications of this result. We also highlight a few examples of complex nuclear morphologies, including double nuclei, extended stellar structures, and nuclear F606W excess from either recent (circum-)nuclear star formation and/or a weak active galactic nucleus. Such examples may serve as case studies for ongoing NSC evolution via the two main suggested mechanisms, namely cluster merging and in situ star formation.