Now scientists believe they have overcome the problem using technology inspired by photosynthesis in plants.
The system allows small amounts of electricity from solar panels to split water into hydrogen and oxygen. A similar water-splitting reaction occurs during photosynthesis. Later, the gases can be recombined in a fuel cell to produce carbon-free electricity.
Electolysers which split water are already used industrially, but are extremely costly and do not work in everyday conditions.
The new process is cheap and operates at room temperature, with neutral acidity water.
Professor Daniel Nocera, from the Massachusetts Institute of Technology in Boston, who co-led the research, said: "Solar power has always been a limited, far-off solution. Now we can seriously think about solar power as unlimited, and soon."
British expert Professor James Barber, from Imperial College London, said the technology represented a "giant leap" towards generating clean, carbon-free energy on a massive scale.
"This is a major discovery with enormous implications for the future prosperity of humankind," he said. "It opens up the door for developing new technologies for energy production thus reducing our dependence for fossil fuels and addressing the global climate change problem."
More work needs to be done to integrate the new technology into existing solar power systems. But Prof Nocera believes that within 10 years people will be able to power their homes with a combination of solar panels and household fuel cells.