A comparative analysis of global river basins shows that some river discharges are more sensitive to future climate change for the coming century than to natural climate variability over the last 9000 years. In these basins (Ganges, Mekong, Volta, Congo, Amazon, Murray-Darling, Rhine, Oder, Yukon) future discharges increase by 6--61%. These changes are of similar magnitude to changes over the last 9000 years. Some rivers (Nile, Syr Darya) experienced strong reductions in discharge over the last 9000 years (17--56%), but show much smaller responses to future warming. The simulation results for the last 9000 years are validated with independent proxy data.