We report results from the Supernova Photometric Classification Challenge (SNPhotCC), a publicly released mix of simulated supernovae (SNe), with types (Ia, Ibc, and II) selected in proportion to their expected rates. The simulation was realized in the griz filters of the Dark Energy Survey (DES) with realistic observing conditions (sky noise, point-spread function, and atmospheric transparency) based on years of recorded conditions at the DES site. Simulations of non-Ia-type SNe are based on spectroscopically confirmed light curves that include unpublished non-Ia samples donated from the Carnegie Supernova Project (CSP), the Supernova Legacy Survey (SNLS), and the Sloan Digital Sky Survey-II (SDSS-II). A spectroscopically confirmed subset was provided for training. We challenged scientists to run their classification algorithms and report a type and photo-z for each SN. Participants from 10 groups contributed 13 entries for the sample that included a host-galaxy photo-z for each SN and nine entries for the sample that had no redshift information. Several different classification strategies resulted in similar performance, and for all entries the performance was significantly better for the training subset than for the unconfirmed sample. For the spectroscopically unconfirmed subset, the entry with the highest average figure of merit for classifying SNe Ia has an efficiency of 0.96 and an SN Ia purity of 0.79. As a public resource for the future development of photometric SN classification and photo-z estimators, we have released updated simulations with improvements based on our experience from the SNPhotCC, added samples corresponding to the Large Synoptic Survey Telescope (LSST) and the SDSS-II, and provided the answer keys so that developers can evaluate their own analysis.