We present the results of a systematic numerical study of an alternative progenitor scenario to produce Type Ia supernova explosions, which is not restricted to the ignition of a CO white dwarf (WD) near the Chandrasekhar mass. In this scenario, a shock-triggered thermonuclear explosion ensues from the collision of two WDs. Consistent modeling of the gas dynamics together with nuclear reactions using both a smoothed particle and a grid-based hydrodynamics code are performed to study the viability of this alternative progenitor channel. We find that shock-triggered ignition and the synthesis of Ni are in fact a natural outcome for moderately massive WD pairs colliding close to head-on. We use a multi-dimensional radiative transfer code to calculate the emergent broadband light curves and spectral time series of these events. The synthetic spectra and light curves compare well to those of normal Type Ia supernovae over a similar B-band decline rate and are broadly consistent with the Phillips relation, although a mild dependence on viewing angle is observed due to the asymmetry of the ejected debris. While event rates within galactic centers and globular clusters are found to be much too low to explain the bulk of the Type Ia supernovae population, they may be frequent enough to make as much as a one percent contribution to the overall rate. Although these rate estimates are still subject to substantial uncertainties, they do suggest that dense stellar systems should provide upcoming supernova surveys with hundreds of such collision-induced thermonuclear explosions per year.