We present the results of a deep, wide area, optical and near-IR survey of massive high-redshift galaxies. The Suprime-Cam on the Subaru telescope was used to obtain BRIz' imaging over 2 × 940 arcmin2 fields, while JKs imaging was provided by the SOFI camera at the New Technology Telescope (NTT) for a subset of the area, partly from the EIS. In this paper, we report on the properties of K-band-selected galaxies, identified from a total area of ~920 arcmin2 to KVega = 19, of which 320 arcmin2 are complete to KVega = 20. The BzK selection technique was used to assemble complete samples of about 500 candidate massive star-forming galaxies (sBzKs) and about 160 candidate massive passively evolving galaxies (pBzKs) at 1.4 ≲ z ≲ 2.5; and the (R - K)Vega > 5 color criterion was used to assemble a sample of about 850 extremely red objects (EROs). We accurately measure surface densities of 1.20 ± 0.05 and 0.38 ± 0.03 arcmin-2 for the sBzKs and the pBzKs, respectively. Both sBzKs and pBzKs are strongly clustered, at a level at least comparable to that of EROs, with pBzKs appearing more clustered than sBzKs. We estimate the reddening, star formation rates (SFRs), and stellar masses (M*) for the ensemble of sBzKs, confirming that to KVega ~ 20 typical (median) values are M* ~ 1011 M☉, SFR ~ 190 M☉ yr-1, and E(B - V) ~ 0.44. A correlation is detected such that the most massive galaxies at z ~ 2 are also the most actively star-forming, an effect that can be seen as a manifestation of downsizing at early epochs. The space density of massive pBzKs at z ~ 1.4-2 that we derive is 20% ± 7% that of similarly massive early-type galaxies at z ~ 0. Adding this space density to that of our massive star-forming class, sBzKs, in the same redshift range produces a closer comparison with the local early-type galaxy population, naturally implying that we are detecting star formation in a sizable fraction of massive galaxies at z > 1.4, which has been quenched by the present day. Follow-up optical and near-infrared spectroscopy is in progress at the ESO Very Large Telescope (VLT) and at the Subaru telescope in order to elucidate more thoroughly the formation and evolution of massive galaxies.