Core impurity transport has been investigated for a variety of confinement regimes in Alcator C-Mod plasmas from x-ray emission following injection of medium and high Z materials. In ohmic L-mode discharges, impurity transport is anomalous (Deff蠑Dnc) and changes very little across the LOC/SOC boundary. In ion cyclotron range of frequencies (ICRF) heated L-mode plasmas, the core impurity confinement time decreases with increasing ICRF input power (and subsequent increasing electron temperature) and increases with plasma current. Nearly identical impurity confinement characteristics are observed in I-mode plasmas. In enhanced Dα H-mode discharges the core impurity confinement times are much longer. There is a strong connection between core impurity confinement time and the edge density gradient across all confinement regimes studied here. Deduced central impurity density profiles in stationary plasmas are generally flat, in spite of large amplitude sawtooth oscillations, and there is little evidence of impurity convection inside of r/a=0.3 when averaged over sawteeth.