The droplets propel themselves over metal sheets scored with a carefully designed array of grooves.
The US scientists did the experiment to demonstrate how the random motion of water molecules in hot steam could be channelled into a directed force.
But the team, writing in Physical Review Letters, believes the effect may be useful in driving coolants through overheating computer microchips.
The physics at work here has been witnessed by all of us in the kitchen.
Leave an empty pan on the stove for too long, and water, when you drip it over the scorching pan bottom, will hover over the surface on a bed of steam.
The effect was described in the 18th Century by a German scientist Johann Gottlob Leidenfrost.
What happens is that the heat is so intense, it boils the underside of the water droplet without any physical contact with the pan.
"We were interested in whether it would be possible to use this phenomenon to move liquids around," said Dr Heiner Linke, the intellectual power behind the self-propelled droplets.
An uphill struggle
The trick seems simple. Instead of using a smooth surface, the team scored it with a series of skewed triangular grooves. This gives it a kind of saw-tooth profile.
Now the water droplets appear to push themselves off the long-slope side of the grooves and rocket across the heated surface - instead of just dancing on the spot as they do in the kitchen pan.
The mechanism is a little more complicated and took a while to work out, Dr Linke told the BBC. "The vapour," he explained, "mostly flows in one direction, and the droplet sits on the flowing vapour, a bit like a boat carried along in a flowing river."
Droplets can also climb over steps, and up inclines of up to 12 degrees. Filmed with high-speed cameras, the droplets appear to take on a life of their own, sliding along like sloppy amoebae.
Although the original intention was to devise an arresting demonstration of how random energy can be rectified into directed motion - the focus of Dr Linke's main work is with molecular motors - the researchers now think there may be a use for the effect in cooling computer microchips.
The electrical currents now passing through microprocessors are so large the heat they generate can limit computing performance.
Many chips have cooling circuits nowadays, but these require pumps to drive the coolant, which in turn generate even more heat.
Suitably micro-patterned channels, argues Dr Linke, would make the coolant flow automatically.
"It would be very neat if we could use the heat from the chip to be the pump, because you would not need any additional power, but also because the pumping only happens when the thing is warm; it would also be a thermostat at the same time. So it would all be in one package."
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