The phase-field method has become the method of choice for simulating microstructure formation during solidification. Recent progress, both on the formulation of the model and on the numerical implementation, makes it now possible to simulate quantitatively the evolution of complex microstructures in three dimensions. This is illustrated by simulations of eutectic coupled growth. The morphological stability of lamellar patterns is investigated, and the results are compared to experimental data obtained by in situ observations of the transparent alloy carbontetrabromide-hexachloroethane. When the lamellar spacing exceeds a critical value, a zigzag instability occurs. The further evolution of the system leads to stable zigzag structures or lamella breakup, depending on the parameters.