This is the first paper in a series presenting and analyzing data for a k-selected sample of galaxies collected in order to identify and study galaxies at moderate to high redshift in rest-wavelength optical light. The sample contains 84 objects over six separate fields covering 75.6 arcmin2down to K = 20-20.5. We combine the K band with UBVRIzJH multiband imaging, reaching depths of R ∼ 26. Two of the fields studied also have deep HST WFPC2 imaging, totaling more than 60 hr in the F300W, F450W, F606W, and F814W filters. Using artificial galaxy modeling and extraction, we measure 85% completeness limits down to K = 19.5-20,dependingonthefieldexamined. The derived K-band number counts are in good agreement with previous studies. We find a density for extremely red objects (EROs; R - K > 5) of 1.55 ±0.16 arcmin"2 for A; < 19.7, dominated by the 1714+5015 field (centered on 53w002), with an ERO number density more than 3 times that of the other sample fields. If we exclude the counts for 1714+5015, our density is 0.95 ± 0.14 arcmin"2. Both ERO densities are consistent with previous measurements due to the significant known cosmic variance of these red sources. Keck spectroscopic redshifts were obtained for 18 of the EROs, all but one of which are emission galaxies. None of the EROs in the 1714+5015 field for which we obtained spectroscopic redshifts are associated with the known z = 2.39 overdensity, although there are three different galaxy redshift pairs (z = 0.90,1.03, and 1.22). © 2006. The American Astronomical Society. All rights reserved.