We have performed three-dimensional MHD equilibrium jet simulations that have been designed to excite the Kelvin-Helmholtz (K-H) instability and allow us to investigate the spatial growth of the mixing layer between a magnetized jet and an initially unmagnetized external medium. These simulations differ in the magnetic field strength and orientation, in the jet-to-ambient density ratio, and in the amplitude of the initial (velocity) perturbation. We calculate as a direct measure of mass entrainment the mass of magnetized or high axial velocity material and compare the growth of entrained mass with dynamical and potentially observable properties of a jet. An equipartition toroidal field (whose magnetic pressure is approximately equal to the jet's thermal pressure) can inhibit the growth of the K-H instability and reduce mass entrainment significantly. An equipartition axial field has a slight stabilizing effect and reduces mass entrainment relative to a weak field for comparable magnetosonic Mach number. As the jet and ambient medium are mixed, the width of simulated total synchrotron intensity images increases and the fractional polarization of the jet decreases. In these simulations the jet evolves to a fast-moving magnetized spine surrounded by a slower moving, less magnetized sheath. These centralized spines are more easily disrupted in jets less dense than the surrounding medium. As a consequence of their greater instability, simulations with axial magnetic fields are more likely than simulations with toroidal magnetic fields to filament into axial (matter) streams. In both the width of the simulated intensity images and in the mass of magnetized material, we see evidence for a linear growth stage, a nonlinear growth stage, and a final saturation stage. Results from a normal-mode analysis suggest that the initial linear stage of mixing coincides with growth of the K-H-unstable normal surface modes and a spatial progression from higher to lower order modes. The nonlinear stage coincides with large-amplitude elliptical distortion to the jet cross section and filamentation of the jet. A subset of simulations was run at lower (9 zones/jet radius) and higher (25 zones/jet radius) spatial resolutions than the typical moderate spatial resolution of 15 zones/jet radius. We find that the instability saturates at approximately the same amount of entrained mass (relative to the jet mass) in the moderate- and high-resolution cases, although the transition between the linear and nonlinear stages is closer to the inlet in the higher resolution simulations.