We have performed new 1.4 GHz and 5 GHz observations of the Local Group galaxy M33 with the Jansky Very Large Array. Our survey has a limiting sensitivity of 20 uJy (4-sigma) and a resolution of 5.9 arcsec (FWHM), corresponding to a spatial resolution of 24 pc at 817 kpc. Using a new multi-resolution algorithm, we have created a catalog of 2875 sources, including 675 with well-determined spectral indices. We detect sources at the position of 319 of the X-ray sources in the Tuellmann et al. (2011) Chandra survey of M33, the majority of which are likely to be background galaxies. The radio source coincident with M33 X-8, the nuclear source, appears to be extended. Along with numerous H II regions or portions of H II region complexes, we detect 155 of the 217 optical supernova remnants included in the lists of Long et al. (2010) and Lee & Lee (2014), making this by far the largest sample of remnants at known distances with multiwavelength coverage. The remnants show a large dispersion in the ratio of radio to X-ray luminosity at a given diameter, a result that challenges the current generation of models for synchrotron radiation evolution in supernova remnants. See http://sundog.stsci.edu/m33 for access to catalogs and images.