Calculations of the electronic mobility and drift velocity have been carried out for bulk GaN and AlGaN-GaN heterojunctions based on a Monte Carlo approach. The bulk calculations were intended to serve as a validity check of the simulation model. For the heterojunction electron mobility calculations, polarization effects, degeneracy, and interface roughness scattering were all taken into account. Degeneracy is shown to play an important role, especially at large gate bias. Very good agreement with available experiments has been obtained, and yields a set of best-fit transport parameters. Our results underscore the dominance of interface roughness scattering, and demonstrate that a parameterized model based on weak-perturbation, Born approximation theory can yield sufficiently accurate results.