The wire medium is a type of complex artificial material we conceptually envision as many identical finite-length, parallel, thin wire inclusions embedded within a host medium. It is representative of a class of novel artificial materials characterized by long thin inclusions. Unlike some conventional artificial material, the inclusions of this class are not necessarily electrically short. Here, we present our theoretical analysis for wire media and by studying certain salient features of plane-wave propagation through these media, introduce equivalent medium parameters that depend, among other parameters, on the direction of wave propagation. The approach we use separates the artificial material into its elementary planes and then uses periodic moment method techniques to individually characterize each elementary plane. Analytic formulas from periodic structure theory are then used to determine the effective wavenumber for the overall medium and the transverse impedance at the midpoint between adjacent elementary planes. Our examples show that some realizations of these media are spatially dispersive and may exhibit interesting features such as "angular windows of propagation" and other properties that are dependent on the polarization, frequency and direction of wave propagation.