Explosions of sub-Chandrasekhar-mass white dwarfs (WDs) are one alternative to the standard Chandrasekhar-mass model of Type Ia supernovae (SNe Ia). They are interesting since binary systems with sub-Chandrasekhar-mass primary WDs should be common and this scenario would suggest a simple physical parameter which determines the explosion brightness, namely the mass of the exploding WD. Here we perform one-dimensional hydrodynamical simulations, associated post-processing nucleosynthesis, and multi-wavelength radiation transport calculations for pure detonations of carbon-oxygen WDs. The light curves and spectra we obtain from these simulations are in good agreement with observed properties of SNe Ia. In particular, for WD masses from 0.97 to 1.15 Msun we obtain 56Ni masses between 0.3 and 0.8 Msun, sufficient to capture almost the complete range of SN Ia brightnesses. Our optical light curve rise times, peak colors, and decline timescales display trends which are generally consistent with observed characteristics although the range of B-band decline timescales displayed by our current set of models is somewhat too narrow. In agreement with observations, the maximum light spectra of the models show clear features associated with intermediate-mass elements and reproduce the sense of the observed correlation between explosion luminosity and the ratio of the Si II lines at ?6355 and ?5972. We therefore suggest that sub-Chandrasekhar-mass explosions are a viable model for SNe Ia for any binary evolution scenario leading to explosions in which the optical display is dominated by the material produced in a detonation of the primary WD.