Battery technology is going to be extremely important to our future. If someone just came up with a rechargeable battery that improved the energy density of lithium-ion cells by a factor of, say, about six, the effects would be tremendous. It wouldn’t just suddenly make the electric car really competitive with fossil-fuel powered cars, it could pretty near wipe out small internal combustion engines altogether. Motor scooters, lawnmowers, and chainsaws would go electric, as would heavy trucks and buses. Diesel would be for ships and locomotives, not for anything on the roads. The reduction of air pollution would be dramatic. Vacuum cleaners would go cordless.
We could build robots that could walk around for longer than fifteen minutes before needing to plug themselves in. We could make strength-enhancing exoskeletons. All kinds of high powered portable doodads.
Also, the economics of shifting from fossil fuels to renewables would become a lot more attractive than they already are.