In collisionless plasmas, the particle distributions are often far from local thermodynamic equilibrium, providing a significant source of free energy that leads to complex velocity-space dynamics. In plasmas driven to turbulence, the possibility of a cascade of the free energy in velocity space, analogous to the spatial cascade of fluid and electromagnetic field energies, has been suggested. However, observational evidence of plasma turbulence in the entire phase space has not been well established. Using measurements from the Magnetospheric Multiscale mission in a special campaign in the Earth’s magnetosheath, we present for the first time a statistical study of velocity-space turbulence in a wide range of plasma conditions. We observe two predicted power laws in the ion velocity-space spectrum – an isotropic -3/2 spectrum and an anisotropic -2 spectrum distinguished by the ion β and bulk flow. In addition, the spectral power laws in the spatial and velocity domains are independent. However, higher energy transfer rates in the magnetic field are correlated with more prominent velocity-space turbulence. Our results ultimately demonstrate that when plasmas are strongly turbulent, the energy transfer occurs both in space and in velocity, thus influencing the energy partition between thermal and non-thermal particles in space and astrophysical plasmas.