We studied the transport and low-field mobility properties of bulk InN and a two-dimensional electron gas confined in an InGaN/GaN quantum well with regard to various parameters such as well width and interface roughness as a function of temperature. Since new material parameters for InN have been suggested by recent studies, the traditionally accepted and recently published parameter values for InN are used in our simulations and the results are compared. Mobility values in two and three dimensions are found from the steady-state drift velocities of carriers calculated using an ensemble Monte Carlo technique. Electron transport properties of bulk GaN and AIN are also presented and compared with bulk InN and InGaN/GaN quantum wells. The mobility of carriers in two dimensions is about 10,000 cm(2)/V s for low temperatures and in bulk InN increases significantly to a value of about 6,450 cm(2)/V s at room temperature when recently established material parameters are used.