We investigate the evolution of protoplanets with different masses embedded in an accretion disk, via global fully three-dimensional hydrodynamical simulations. We consider a range of planetary masses extending from 1.5 M_⊕ up to 1 M_J, and we take into account physically realistic gravitational potentials of forming planets. In order to calculate accurately the gravitational torques exerted by disk material and to investigate the accretion process onto the planet, the flow dynamics has to be thoroughly resolved on long as well as short length scales. We achieve this strict resolution requirement by applying a nested-grid refinement technique that allows us to greatly enhance the local resolution. Our results from altogether 51 simulations show that for large planetary masses, approximately above 0.1 M_J, migration rates are relatively constant, as expected in a type II migration regime and in good agreement with previous two-dimensional calculations. In a range between 7 and 15 M_⊕, we find a dependency of the migration speed on the planetary mass that yields timescales considerably longer than those predicted by linear analytical theories. This property may be important in determining the overall orbital evolution of protoplanets. The growth timescale is minimum around 20 M_⊕, but it rapidly increases for both smaller and larger mass values. Significant differences between two- and three-dimensional calculations are found in particular for objects with masses smaller than 10 M_⊕. We also derive an analytical approximation for the numerically computed mass growth rates.