Phonon-limited mobilities of electrons and holes in Si nanowires (NWs) with 〈001〉, 〈110〉, and 〈111〉 orientations are calculated in a fully atomistic framework for diameters up to 10 nm. Electron-phonon scattering rates are computed with an sp3d5s* tight-binding model for electrons and a valence-force field model for phonons. The Boltzmann equation is then solved exactly for the low-field mobility. Compared to bulk Si, the electron mobilities are strongly reduced, but the hole mobilities can be enhanced in 〈111〉 and 〈110〉 NWs with diameters around 3.5 nm. The mobility, however, rapidly decreases with carrier concentration > 1019 cm-3.