Anomalous momentum transport has been observed in Alcator C-Mod tokamak plasmas. The time evolution of core impurity toroidal rotation velocity profiles has been measured with a tangentially viewing crystal x-ray spectrometer array. Following the L-mode to EDA (enhanced Dα) H-mode transition in both Ohmic and ion cyclotron range of frequencies heated discharges, the ensuing co-current toroidal rotation velocity, which is generated in the absence of any external momentum source, is observed to propagate in from the edge plasma to the core with a timescale of the order of the observed energy confinement time, but much less than the neo-classical momentum confinement time. The ensuing steady state toroidal rotation velocity profiles in EDA H-mode plasmas are relatively flat, with Vϕ ∼ 50 km s−1, and the momentum transport can be simulated using a simple diffusion model. Assuming that the L–H transition produces an instantaneous edge source of toroidal torque (which disappears at the H- to L-mode transition), the momentum transport may be characterized by a diffusivity, with values of ∼0.07 m2 s−1 during EDA H-mode and ∼0.2 m2 s−1 in L-mode. These values are large compared to the calculated neo-classical momentum diffusivities, which are of the order of 0.003 m2 s−1. Velocity profiles of ELM-free H-mode plasmas are centrally peaked (with Vϕ(0) exceeding 100 km s−1 in some cases), which suggests the presence of an inward momentum pinch; the observed profiles are consistent with simulations including an edge inward convection velocity of ∼10 m s−1. In EDA H-mode discharges which develop internal transport barriers, the velocity profiles become hollow in the centre, indicating the presence of a negative radial electric field well in the vicinity of the barrier foot. Upper single null diverted and inner wall limited L-mode discharges exhibit strong counter-current rotation (with Vϕ(0)∼−60 km s−1 in some cases), which may be related to the observed higher H-mode power threshold in these configurations. For plasmas with locked modes, the toroidal rotation is observed to cease (Vϕ ⩽ 5 km s−1).