A phase field concept for interface motion in general multi-phase systems with anisotropic interfacial energy is studied. We allow the anisotropy to be even crystalline which leads to a polygonial Wulff shape. A sharp interface model which appears as the limit of small interfacial thickness is stated. Through a series of numerical simulations we demonstrate that our concept can recover features like crystalline curvature flow, an anisotropic version of Young's law at triple-junctions and an anisotropic modification of the right angle condition at points where the interface intersects an external boundary. An important advantage of our approach is that there is a simple relation between the coefficients in the phase field model and the defining parameters of the sharp interface model.