We present medium-resolution (R~700) near-infrared (lambda=1-2.5m) 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: HI emission line-dominated PNe, HI 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 toward 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.