Precognition was the ability to perceive events which had not yet happened, sometimes in prophecies.
As with other "paranormal" phenomena, the presence of a time fissure could enable humans to develop precognitive powers. The Fourth Doctor attributed the special powers possessed by Ma Tyler (respected by locals as a witch) to the fact that she had always lived near such a time fissure. (TV: Image of the Fendahl)
Other instances Edit
Gwen Cooper had a precognitive vision of the stabbing death of her boyfriend, Rhys. She managed to prevent the event in the location in which she saw his death as having occurred, but could not prevent his death from happening elsewhere. (TV: End of Days)
The soothsayers of Pompeii, due to their minds being opened up to have psychic powers and the explosion of Vesuvius opening a rift in time for a second which echoed back through time, developed precognitive powers (TV: The Fires of Pompeii) and everything they predicted came true, including the return of Rose Tyler and the Time Beetle on Donna Noble's back. (TV: Turn Left) This power disappeared after the volcano erupted — Evelina could no longer see the future as the Pyroviles were dead and the rift had passed. (TV: The Fires of Pompeii)
The Ood, who possessed telepathic abilities, showed some precognition, with Ood Sigma predicting that the Doctor's song was ending (referring to his impending regeneration into the Eleventh Doctor) and later, when time was bleeding, they were able to predict the return of the Master, Gallifrey, the Time Lords and that Joshua Naismith was important to what was going on. (TV: Planet of the Ood, The End of Time)
Carmen, who possessed psychic abilities, predicted the Doctor's coming death telling him that "it (Gallifrey) is returning" and that "he (Wilfred Mott) will knock four times." (TV: Planet of the Dead)
The people of Eve were a time-sensitive race and were able to read timelines (i.e. seeing the past and reading the future). However, they were all but exterminated in the Last Great Time War . (TV: The Mad Woman in the Attic)