We report the results of a near-infrared (mostly K-band) spectroscopic survey of planetary nebulae at McDonald Observatory during the period 1986-1993. These observations were made with a grating spectrometer based on a 1 × 32-element InSb array. Most of the K-band observations were taken with spectral resolving power R = λ/Δλ = 600 in order to resolve the v=1-0 S(1) 2.121 μm H2 line from the adjacent recombination line of He I at 2.113 μm. We also simultaneously measured the strengths of H I Br γ and He II 2.189 μm. The typical limiting line flux detected in our 3.8″ beam was 1-3 × 10–14 erg cm–2 s–1, corresponding to a surface brightness of 3 × 10–5 to 1 × 10–4 erg cm–2 s–1 ster–1. An early result of this study was the first conclusive proof that the UV-pumping or “fluorescence” mechanism, rather than thermal (shock) excitation, is responsible for the H2 emission in a planetary nebula, Hubble 12 (Dinerstein et al. 1988, ApJ, 327, L27). This was also one of the first demonstrated cases of UV-pumped H2 emission in any astronomical source, and Hubble 12 has become a template for the study of this emission mechanism.