We present results from three-dimensional (3-D) Cartesian geometry computations featuring vigorous (high Rayleigh number) mantle convection in a system incorporating stiff tectonic plates with dynamically determined, time-dependent velocities. We track plume-related hot spot motion while calculating associated synthetic hot spot tracks, allowing us to estimate plume migration rates relative to plate motion rates. Plate-like surface motion is achieved explicitly by specifying both the plate geometry and rigidity; however, plate velocities evolve dynamically in response to the buoyancy distribution within the convecting system, including buoyancy within the plate itself. We find that convection is characterized by downwelling sheets and varying numbers of 3-D upwelling structures when the lower mantle to upper mantle viscosity ratio is varied from 9 to 90. As the lower mantle viscosity is increased relative to the upper mantle viscosity, the upwellings in the calculations evolve into vigorous (active) plumes characterized by long, narrow, thermal conduits with broad, disk-like heads. The total number, shape, and persistence of the plumes are affected by the specified viscosity stratification in the calculations. Our findings indicate that hot spots associated with mantle plumes drift by smaller distances in comparable amounts of time when the lower mantle viscosity is increased relative to the upper mantle viscosity. In cases with a high lower mantle to upper mantle viscosity ratio, the depth of the flow aligned with plate motion is diminished and the plate-scale return flow is integrated into a deep, unorganized, sluggish layer. As a result, plume conduit morphology in the lower mantle of such calculations is less influenced by plate motion than in calculations with a small difference between upper mantle and lower mantle viscosity. For lower mantle viscosities 30 times and 90 times greater than the upper mantle viscosity, the lower mantle velocity field is dominated locally by active plumes anchored in the lower thermal boundary layer of the convecting system and plume migration rates are typically only about 10% of the overriding plate velocity. In such cases, we also find that plume-related hot spots persist for periods that we estimate to be between 0.55 and 1.1 plume-transit times.