Large numbers of supernovae (SNe) have been discovered in recent years, and many more will be found in the near future. Once discovered, further study of a SN and its possible use as an astronomical tool (e.g., as a distance estimator) require knowledge of the SN type. Current classification methods rely almost solely on the analysis of SN spectra to determine their type. However, spectroscopy may not be possible or practical. We present a classification method for SNe based on the comparison of their observed colors with synthetic ones, calculated from a large database of multi-epoch optical spectra of nearby events. Broadband photometry at optical wavelengths allows classification of SNe up to z = 0.75, and the use of infrared bands extends it further to z = 2.5. We demonstrate the applicability of this method, outline the observational data required to further improve the usefulness of the method, and discuss prospects for its use on future SN samples. Community access to the tools developed is provided by a dedicated website.