The static and dynamic properties of coupled one-dimensional (1D) and two-dimensional (2D) periodic Ni80Fe20 structures fabricated using deep ultraviolet lithography were systematically studied using broadband ferromagnetic resonance spectroscopy, magneto-optical Kerr effects measurements, and magnetic force microscopy. We have probed the influence of dipolar coupling on the spin configurations and magnetization reversal mechanisms in three different types of magnonic crystals, namely, a 1D chain of coupled ellipsoids arranged in two basic configurations (elements coupled along the major or minor axis) and a 2D noncollinear array of rectangular elements. We observed that the “collective” modes present in the spin wave spectrums for the array are significantly dependent on the geometrical parameters of the magnetic elements, as well as on their arrangement. For instance, the eigenmodes corresponding to the linear chain of ellipsoidal elements are considerably shifted when compared to a continuous film due to the varying demagnetizing field. However, for 2D periodic magnetic structures in which the elements are arranged in a “C” cell configuration with each unit cell comprising of three rectangular elements, we observed the presence of two distinct eigenmodes that vary with the magnitude and orientation of the applied field.