To mitigate anthropogenically induced climate change and ocean acidification, net carbon dioxide emissions to the atmosphere must be reduced. One proposed option is underground CO2 disposal. Large-scale injection of CO2 into the Earth's crust requires an understanding of the multiphase flow properties of high-pressure CO2 displacing brine. We present laboratory-scale core flooding experiments designed to measure CO2 endpoint relative permeability for CO2 displacing brine at in situ pressures, salinities, and temperatures. Endpoint drainage CO2 relative permeabilities for liquid and supercritical CO2 were found to be clustered around 0.4 for both the synthetic and natural media studied. These values indicate that relative to CO2, water may not be strongly wetting the solid surface. Based on these results, CO2 injectivity will be reduced and pressure-limited reservoirs will have reduced disposal capacity, though area-limited reservoirs may have increased capacity. Future reservoir-scale modeling efforts should incorporate sensitivity to relative permeability. Assuming applicability of the experimental results to other lithologies and that the majority of reservoirs are pressure limited, geologic carbon sequestration would require approximately twice the number of wells for the same injectivity.