Gorgon

The Gorgons were a species of intelligent parasitic beings which possessed their hosts.

Biology
Gorgons looked like blue, ethereal serpents. Each Gorgon was composed of several of these serpentine forms. They could hiss but not speak. They had some telepathic powers, specifically mind control.

Gorgons petrified living creatures within a matter of hours. To do so, they needed to leave their host and make contact with the target. They could be reflected by a mirror, causing them to return to the host and turning it to stone.

Gorgons were a species of parasites, inhabiting the bodies of creatures like humans. While in the host, they greatly increased its lifespan, letting one human host live for over two hundred years. This was much less than the Gorgon's natural lifespan of thousands of years, which meant they had to frequently switch hosts. (TV: Eye of the Gorgon)

History
Three Gorgons came to Earth around 1000 BC via a talisman, entering into Greek mythology along the way. One Gorgon was slain by a Greek hero, another by Professor Nelson-Stanley and his wife in 1959, and the other survived up until the 21st century.

The third Gorgon eventually inhabited the body of an abbess and led the sisterhood of nuns at St Agnes Abbey, manipulating their minds to serve it for more than two centuries. The Gorgon sent the nuns to retrieve the talisman, planning to call the Gorgons from their home world to invade Earth and take all of humanity for their hosts. The Gorgon was defeated by Sarah Jane, Luke, Maria and Clyde, using a mirror to defeat the Gorgon whilst trying to possess Sarah Jane as a new host. (TV: Eye of the Gorgon)

Alternate timeline
In Andrea Yates' World, where the Trickster manipulated events so that Sarah Jane Smith died in 1964, the Gorgons never came to Earth. As the Trickster explained to Sarah Jane while she was in limbo, he had turned away all the foes she would have defeated, his intention being for her absence to allow Earth to be destroyed by the meteorite K67. (TV: Whatever Happened to Sarah Jane?)