The general properties of the nonthermal nonpulsed X-ray emission of rotation-powered pulsars are investigated in the context of a pulsar wind nebula model. An examination of the observed X-ray emission from a sample of 23 pulsars in the energy range between 2 and 10 keV reveals that the relation of X-ray luminosity, L sub(X), to the pulsar spin-down power, E, is steeper for the nonpulsed component than for the pulsed component. Specifically, L super(n) sub(X) super(pul) 8 E super(1.4c0.1) for the nonpulsed component, whereas L super(p) sub(X) super(ul) 8 E super(1.2c0.08) for the pulsed component. The former relation is consistent with emission from a pulsar wind nebula model in which L super(n) sub(X) super(pul) 8 E super(p/2), where p is the power-law index of the electron energy distribution. The relation for the pulsed component, on the other hand, is consistent with a magnetospheric emission model. In addition, the photon spectral index, , was found to be correlated with the conversion efficiency of spin-down power into nonpulsed X-ray emission, with greater efficiencies for 6 2-2.5 than for 6 1.5-2. Such a relation can be naturally understood within the framework of a pulsar wind nebula model, with the former relation corresponding to the emission of X-rays in the fast-cooling regime and the latter relation corresponding to emission in the slow-cooling regime. The X-ray properties of pulsar wind nebulae are sensitive to the physical conditions (e.g., the density and magnetic field) of the interstellar medium, which can lead to important differences between the X-ray emission characteristics (luminosity, photon spectral index, and emission morphology) of pulsars in various environments. Such wind nebulae can contribute to the nonthermal symmetric emission morphology (pointlike) and elongated emission morphology (tail-like) from sources similar to Geminga and PSR B1757-24.