Massive quiescent galaxies at z > 1 have been found to have small physical sizes, and hence to be superdense. Several mechanisms, including minor mergers, have been proposed for increasing galaxy sizes from high- to low-z. We search for superdense massive galaxies in the WIde-field Nearby Galaxy-cluster Survey (WINGS) of X-ray selected galaxy clusters at 0.04 < z < 0.07. We discover a significant population of superdense massive galaxies with masses and sizes comparable to those observed at high redshift. They approximately represent 22% of all cluster galaxies more massive than 3 × 1010 M sun, are mostly S0 galaxies, have a median effective radius langRe rang = 1.61 ± 0.29 kpc, a median Sersic index langnrang = 3.0 ± 0.6, and very old stellar populations with a median mass-weighted age of 12.1 ± 1.3 Gyr. We calculate a number density of 2.9 × 10-2 Mpc-3 for superdense galaxies in local clusters, and a hard lower limit of 1.3 × 10-5 Mpc-3 in the whole comoving volume between z = 0.04 and z = 0.07. We find a relation between mass, effective radius, and luminosity-weighted age in our cluster galaxies, which can mimic the claimed evolution of the radius with redshift, if not properly taken into account. We compare our data with spectroscopic high-z surveys and find that—when stellar masses are considered—there is consistency with the local WINGS galaxy sizes out to z ~ 2, while a discrepancy of a factor of 3 exists with the only spectroscopic z > 2 study. In contrast, there is strong evidence for a large evolution in radius for the most massive galaxies with M * > 4 × 1011 M sun compared to similarly massive galaxies in WINGS, i.e., the brightest cluster galaxies.