We investigate the effect of the mass anisotropy on Friedel oscillations, Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, screening properties, and Boltzmann transport in two-dimensional (2D) metallic and doped semiconductor systems. We calculate the static polarizability and the dielectric function within the random phase approximation with the mass anisotropy fully taken into account without making any effective isotropic approximation in the theory. We find that carrier screening exhibits an isotropic behavior for small momenta despite the anisotropy of the system and becomes strongly anisotropic above a certain threshold momentum. Such an anisotropy of screening leads to anisotropic Friedel oscillations, and an anisotropic RKKY interaction characterized by a periodicity dependent on the direction between the localized magnetic moments. We also explore the disorder limited dc transport properties in the presence of mass anisotropy based on the Boltzmann transport theory. Interestingly, we find that the anisotropy ratio of the short-range disorder limited resistivity along the heavy- and light-mass directions is always the same as the mass anisotropy ratio, whereas for the long-range disorder limited resistivity the anisotropy ratio is the same as the mass ratio only in the low-density limit and saturates to the square root of the mass ratio in the high-density limit. Our theoretical work should apply to many existing and to-be-discovered anisotropic 2D systems.