  We present in this paper an analysis of the faint and red near-infrared
selected galaxy population found in near-infrared imaging from the Palomar
Observatory Wide-Field Infrared Survey. This survey covers 1.53 deg^2 to
5-sigma detection limits of K_vega = 20.5-21 and J_vega = 22.5, and overlaps
with the DEEP2 spectroscopic redshift survey. We discuss the details of this
NIR survey, including our J and K band counts. We show that the K-band galaxy
population has a redshift distribution that varies with K-magnitude, with most
K < 17 galaxies at z < 1.5 and a significant fraction (38.3+/-0.3%) of K > 19
systems at z > 1.5. We further investigate the stellar masses and morphological
properties of K-selected galaxies, particularly extremely red objects, as
defined by (R-K) > 5.3 and (I-K) > 4. One of our conclusions is that the ERO
selection is a good method for picking out galaxies at z > 1.2, and within our
magnitude limits, the most massive galaxies at these redshifts. The ERO limit
finds 75% of all M_* > 10^{11} M_0 galaxies at z ~ 1.5 down to K_vega = 19.7.
We further find that the morphological break-down of K < 19.7 EROs is dominated
by early-types (57+/-3%) and peculiars (34+/-3%). However, about a fourth of
the early-types are distorted ellipticals, and within CAS parameter space these
bridge the early-type and peculiar population, suggesting a morphological
evolutionary sequence. We also investigate the use of a (I-K) > 4 selection to
locate EROs, finding that it selects galaxies at slightly higher average
redshifts (<z> = 1.43+/-0.32) than the (R-K) > 5.3 limit with <z> =
1.28+/-0.23. Finally, by using the redshift distribution of K < 20 selected
galaxies, and the properties of our EROs, we are able to rule out all
monolithic collapse models for the formation of massive galaxies.
