Using a combination of ground-based and HST imaging, we have constructed a catalog of 179 supernova remnants (SNRs) and SNR candidates in the nearby spiral galaxy M51. Follow-up spectroscopy of 66 of the candidates confirms 61 of these as SNRs, and suggests that the vast majority of the unobserved objects are SNRs as well. A total of 55 of the candidates are coincident with (mostly soft) X-ray sources identified in deep Chandra observations of M51; searching the positions of other soft X-ray sources resulted in several additional possible optical candidates. There are 16 objects in the catalog coincident with known radio sources. None of the sources with spectra shows the high velocities (>500 km/s) characteristic of young, ejecta-dominated SNRs like Cas A; instead, most if not all appear to be middle-aged SNRs. The general properties of the SNRs, size distribution and spectral characteristics, resemble those in other nearby spiral galaxies, notably M33, M83, and NGC6946, where similar samples exist. However, the spectroscopically observed [N II]:H{alpha} ratios appear to be significantly higher than in any of these other galaxies. Although we have explored various ideas to explain the high ratios in M51, none of the explanations appears to be satisfactory.