The last comprehensive catalogue of high-mass X-ray binaries in the Small Magellanic Cloud (SMC) was published about ten years ago. Since then new such systems were discovered, mainly by X-ray observations with Chandra and XMM-Newton. For the majority of the proposed HMXBs in the SMC no X-ray pulsations were discovered as yet, and unless other properties of the X-ray source and/or the optical counterpart confirm their HMXB nature, they remain only candidate HMXBs. From a literature search we collected a catalogue of 148 confirmed and candidate HMXBs in the SMC and investigated their properties to shed light on their real nature. Based on the sample of well-established HMXBs (the pulsars), we investigated which observed properties are most appropriate for a reliable classification. We defined different levels of confidence for a genuine HMXB based on spectral and temporal characteristics of the X-ray sources and colour-magnitude diagrams from the optical to the infrared of their likely counterparts. We also took the uncertainty in the X-ray position into account. We identify 27 objects that probably are misidentified because they lack an infrared excess of the proposed counterpart. They were mainly X-ray sources with a large positional uncertainty. This is supported by additional information obtained from more recent observations. Our catalogue comprises 121 relatively high-confidence HMXBs (the vast majority with Be companion stars). About half of the objects show X-ray pulsations, while for the rest no pulsations are known as yet. A comparison of the two subsamples suggests that long pulse periods in excess of a few 100s are expected for the "non-pulsars", which are most likely undetected because of aperiodic variability on similar timescales and insufficiently long X-ray observations. The highest X-ray variability together with the lowest observed minimum fluxes for short-period pulsars indicate that in addition to the eccentricity of the orbit, its inclination against the plane of the Be star circum-stellar disc plays a major role in determining the outburst behaviour. The large population of HMXBs in the SMC, in particular Be X-ray binaries, provides the largest homogeneous sample of such systems for statistical population studies.