A single microscopic magnetic trap for neutral atoms using planar current-carrying wires was proposed and studied theoretically by Weinstein et al. In this paper, we propose three structures of composite current-carrying wires to provide 1D, 2D and 3D arrays of microscopic magnetic traps for cold alkali atoms. The spatial distributions of magnetic fields generated by these structures are calculated and the field gradient and curvature in each single microtrap are analysed. Our study shows that arrays of microscopic magnetic traps can be used to provide 1D, 2D or 3D atomic magnetic lattices and even to realize 1D, 2D and 3D arrays of magneto-optical traps and so on.