We search for massive and compact galaxies (superdense galaxies, hereafter SDGs) at z = 0.03-0.11 in the Padova-Millennium Galaxy and Group Catalogue, a spectroscopically complete sample representative of the general field population of the local universe. We find that compact galaxies with radii and mass densities comparable to high-z massive and passive galaxies represent 4.4% of all galaxies with stellar masses above 3 × 1010 M ⊙, yielding a number density of 4.3 × 10-4 h 3 Mpc-3. Most of them are S0s (70%) or ellipticals (23%), are red, and have intermediate-to-old stellar populations, with a median luminosity-weighted age of 5.4 Gyr and a median mass-weighted age of 9.2 Gyr. Their velocity dispersions and dynamical masses are consistent with the small radii and high stellar mass estimates. Comparing with the WINGS sample of cluster galaxies at similar redshifts, the fraction of SDGs is three times smaller in the field than in clusters, and cluster SDGs are on average 4 Gyr older than field SDGs. We confirm the existence of a universal trend of smaller radii for older luminosity-weighted ages at fixed galaxy mass. As a consequence, the median mass-size relation shifts toward smaller radii for galaxies with older stars, but the effect is much more pronounced in clusters than in the field. Our results show that, on top of the well-known dependence of stellar age on galaxy mass, the luminosity-weighted age of galaxies depends on galaxy compactness at fixed mass and, for a fixed mass and radius, on environment. This effect needs to be taken into account in order not to overestimate the evolution of galaxy sizes from high to low z. Our results and hierarchical simulations suggest that a significant fraction of the massive compact galaxies at high z have evolved into compact galaxies in galaxy clusters today. When stellar age and environmental effects are taken into account, the average amount of size evolution of individual galaxies between high and low z is mild, a factor ~1.6.