We present in this paper a new three-dimensional galaxy classification system designed to account for the diversity of galaxy properties in the nearby universe. To construct this system we statistically analyse a sample of >22 000 galaxies at v < 15 000 km s−1 (z < 0.05) with Spearman rank and principal-component analyses (PCAs). Fourteen major galaxy properties are considered, including: Hubble type, size, colour, surface brightness, magnitude, stellar mass, internal velocities, H i gas content and an index that measures dynamical disturbances. We find, to a high degree, that most galaxy properties are correlated, with in particular Hubble type, colour and stellar mass all strongly related. We argue that this tight three-way correlation is a result of evolutionary processes that depend on galaxy mass, as we show that the relation between colour and mass is independent of Hubble type. Various PCAs reveal that most of the variation in nearby galaxy properties can be accounted for by eigenvectors dominated by (i) the scale of a galaxy, such as its stellar mass, (ii) the spectral type and (iii) the degree of dynamical disturbances. We suggest that these three properties: mass, star formation and interactions/mergers are the major features that determine a galaxy's physical state, and should be used to classify galaxies. As shown by Conselice et al., these properties are measurable within the CAS (concentration, asymmetry, clumpiness) structural system, thus providing an efficient mechanism for classifying galaxies in optical light within a physical meaningful framework. We furthermore discuss the fraction and number density of galaxies in the nearby universe as a function of Hubble type, for comparison with higher redshift populations.