Static electricity was a form of electricity used by many species, most notably the Daleks.

The Daleks used static electricity in their city on Skaro; rather than use an internal power source, they picked up power through the floor. The Doctor, Ian, Barbara and Susan realised this by the smell they made when moving and were reminded of dodgems at a fairground. They disabled a Dalek by pushing it onto a Thal cloak, insulating the Dalek base from the electricity. They then used the empty Dalek shell to escape the city. (TV: The Daleks)

In 1866 on Earth, Edward Waterfield conducted experiments with static electricity and time travel. (TV: The Evil of the Daleks)

During the 22nd century Dalek invasion of Earth, the Daleks used discs on their backs to supply them with static electricity; these required recharging periodically. (TV: The Dalek Invasion of Earth)

On Vulcan, scientist Lesterson found a capsule in a mercury swamp containing three dormant Daleks, which he brought back to life. The Vulcan colony did not have metal floors from which the Daleks could extract static electricity, so they had power cables laid for them to use. (TV: The Power of the Daleks)

While never explicitly stated that the Daleks evolved beyond a need for static electricity, later stories would drop this aspect. In addition, TV: Death to the Daleks would state that the Dalek casing was powered by the Dalek creature's telekinesis.

The Trods were also powered by static electricity. (COMIC: The Trodos Tyranny)

Cessair used a static electrical charge as a primitive but effective force field. (TV: The Stones of Blood)