We discuss the formation of polycrystalline microstructures within the framework of a recently proposed phase field theory. The formation of spherulites is described by an extension of the model that incorporates branching with a definite orientational mismatch. This effect is introduced via a metastable minimum in the orientational free energy. Spherulites are an extreme example of polycrystalline growth, a phenomenon that results from the quenching of orientational defects (grain boundaries) into the solid as the ratio of the rotational to the translational diffusion coefficient is reduced, as is found at high undercoolings. It is demonstrated that a broad variety of spherulitic patterns can be recovered by changing only a few model parameters.