We present deep near-infrared JHK imaging of four 10x10 fields. The observations were carried out as part of the Multiwavelength Survey by Yale-Chile (MUSYC) with ISPI on the CTIO 4m telescope. The typical point source limiting depths are J~22.5, H~21.5, and K~21 (5sigma; Vega). The effective seeing in the final images is ~1.0. We combine these data with MUSYC UBVRIz imaging to create K-selected catalogs that are unique for their uniform size, depth, filter coverage, and image quality. We investigate the rest-frame optical colors and photometric redshifts of galaxies that are selected using common color selection techniques, including distant red galaxies (DRGs), star-forming and passive BzKs, and the rest-frame UV-selected BM, BX, and Lyman break galaxies (LBGs). These techniques are effective at isolating large samples of high redshift galaxies, but none provide complete or uniform samples across the targeted redshift ranges. The DRG and BM/BX/LBG criteria identify populations of red and blue galaxies, respectively, as they were designed to do. The star-forming BzKs have a very wide redshift distribution, a wide range of colors, and may include galaxies with very low specific star formation rates. In comparison, the passive BzKs are fewer in number, have a different distribution of K magnitudes, and have a somewhat different redshift distribution. By combining these color selection criteria, it appears possible to define a reasonably complete sample of galaxies to our flux limit over specific redshift ranges. However, the redshift dependence of both the completeness and sampled range of rest-frame colors poses an ultimate limit to the usefulness of these techniques.
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