We present a study of electron scattering processes in AlGaN/GaN two-dimensional electron gases. A theoretical study of the effect of deformation potential scattering from strain fields surrounding dislocations is presented. The most important scattering mechanisms limiting electron transport are identified. We find that for AlGaN/GaN 2DEGs, mobility is limited by alloy scattering at high 2DEG densities. For AlN/GaN 2DEGs, interface roughness scattering limits mobility at high densities; there is a large improvement by the removal of the alloy barrier. At low 2DEG densities, dislocation scattering from charged cores and strain fields are the dominant scattering mechanisms.