We present a family of six BVI template light curves for SNe Ia for days -5 and +80, based on high-quality data gathered at CTIO. These templates display a wide range of light curve morphologies, with initial decline rates of their B light curves between ∆m15(B)=0.87 m and 1.93. We use these templates to study the general morphology of SNe Ia light curves. We find that several of the main features of the BVI templates correlate tightly with ∆m15(B). In particular, the V light curves, which are probably a reasonably good approximation of the bolometric light curves, display an orderly progression in shapes between the most-luminous, slowest-declining events and the least-luminous, fastest-declining SNe. This supports the idea that the observed spectroscopic and photometric sequences of SNe Ia are due primarily to one parameter. Nevertheless, SNe with very similar initial decline rates do show significant differences in their light curve properties when examined in detail, suggesting the influence of one or more secondary parameters.