We present medium-resolution (R ∼ 700) near-infrared (λ = 1 − 2.5 µm) spectra of a sample of planetary nebulae (PNe). A narrow slit was used which sampled discrete locations within the nebulae; observations were obtained at one or more positions in the 41 objects included in the survey. The PN spectra fall into one of four general categories: H I emission line-dominated PNe, H I and H 2 emission line PNe, H 2 emission line-dominated PNe, and continuum-dominated PNe. These categories correlate with morphological type, with the elliptical PNe falling into the first group, and the bipolar PNe primarily in the H 2 and continuum emission groups. The categories also correlate with C/O ratio, with the O-rich objects generally falling into the first group and the C-rich objects in the other groups. Other spectral features were observed in all categories, such as continuum emission from the central star, C 2 , CN, and CO emission, and warm dust continuum emission towards the long wavelength end of the spectra.Molecular hydrogen was detected for the first time in four PNe. An excitation analysis was performed using the H 2 line ratios for all of the PN spectra in the survey where a sufficient number of lines were observed. From the near-infrared spectrum, we determined an ortho-to-para ratio, the rotational and vibrational excitation temperatures, and the dominant excitation mechanism of the H 2 for many objects surveyed. One unexpected result from this analysis is that the H 2 is excited by absorption of ultraviolet photons in most of the PNe surveyed, although for several PNe in our survey collisional excitation in moderate velocity shocks plays an important role. The correlation between bipolar morphology and H 2 emission has been strengthened with the new detections of H 2 in this survey. We discuss the role of winds and photons to the excitation of H 2 in PNe, and consider some implications to the utility of H 2 as a nebular diagnostic and to our understanding of PNe structure and evolution.