A simple and general method is suggested for studying processes in which resonances or unstable particles are produced. The method consists of analyzing the experimental data in terms of all the possible angular correlations among the decay products of the produced particles. The specific correlations that can be present in a number of experimentally feasible processes are explicitly tabulated. The usefulness of this method of analysis is illustrated by showing how the correlations provide extensive tests of various dynamical models of the production process such as one-particle exchanges. Independent of any models, a great deal can be learned about the production amplitude from just the correlations present when neither incident beam nor target are polarized, although, in general, additional correlations must be known to completely construct this amplitude.