The Herschel Virgo Cluster Survey (HeViCS) is the deepest, confusion-limited survey of the Virgo Cluster at far-infrared (FIR) wavelengths. The entire survey at full depth covers similar to 55 deg(2) in five bands (100-500 mu m), encompassing the areas around the central dominant elliptical galaxies (M87, M86 and M49) and extends as far as the NW cloud, the W cloud and the Southern extension. The survey extends beyond this region with lower sensitivity so that the total area covered is 84 deg(2). In this paper we describe the data, the data acquisition techniques and present the detection rates of the optically selected Virgo Cluster Catalogue (VCC). We detect 254 (34 per cent) of 750 VCC galaxies found within the survey boundary in at least one band and 171 galaxies are detected in all five bands. For the remainder of the galaxies we have measured strict upper limits for their FIR emission. The population of detected galaxies contains early as well as late types although the latter dominate the detection statistics. We have modelled 168 galaxies, showing no evidence of a strong synchrotron component in their FIR spectra, using a single-temperature modified blackbody spectrum with a fixed emissivity index (beta = 2). A study of the chi(2) distribution indicates that this model is not appropriate in all cases, and this is supported by the FIR colours which indicate a spread in beta = 1-2. Statistical comparison of the dust mass and temperature distributions from 140 galaxies with chi(2)(d.o.f.=3) \textless 7.8 (95 per cent confidence level) shows that late types have typically colder, more massive dust reservoirs; the early-type dust masses have a mean of log[\textless M \textgreater/M-circle dot] = 6.3 +/- 0.3, while for late types log[\textless M \textgreater/M-circle dot] = 7.1 +/- 0.1. The late-type dust temperatures have a mean of \textless T \textgreater = 19.4 +/- 0.2 K, while for the early types, \textless T \textgreater = 21.1 +/- 0.8 K. Late-type galaxies in the cluster exhibit slightly lower dust masses than those in the field, but the cluster environment seems to have little effect on the bulk dust properties of early types. In future papers we will focus more on the scientific analysis of the catalogue (e.g. measuring FIR luminosity functions, dust mass functions and resolved gas and dust properties).