Water-powered water pumps
Hydraulic ram water pumps use downhill water pressure to pump water much higher than it started, with no other power needed. A 20ft fall is enough to push water 150 feet above the source or more. Or as little as a 2ft fall between the water source and the pump at a flow rate of 1 to 3 gallons per minute is enough to pump water 20ft higher than the source -- as much as 4,000 gallons a day, depending on the model.
Folk hydraulic ram pump
No modern magic this -- ram pumps were invented more than 300 years ago. A more recent variation is the High Lifter pump, which uses different principles to do the same thing. Ram pumps are noisy, high lifters are silent and can work with less water, but the water has to be clean and grit free, while the ram pump is not so fussy.