Reincarnation

Reincarnation was the belief that someone's spirit was reborn in a new body after the death of the old body.

Metempsychosis was an ancient belief in the migration of the soul after death, held by Pythagoras and his tutor Oenuphis. Pythagoras believed that the Doctor's multiple incarnations were proof of metempsychosis. (PROSE: The Pythagoras Problem)

Attila the Hun thought that Yasmin Khan might have been a reincarnation of Queen Zenobia of Palmyra. (PROSE: Combat Magicks)

The Aztecs believed Barbara Wright to be a reincarnation of Yetaxa. (TV: The Aztecs)

Buddhists believed in reincarnation, specifically that they would be reborn over and over again until they were free from suffering and obtained Nirvana. (AUDIO: The Natural History of Fear)

The Kronteps believed in a form of reincarnation: after a brave death, their spirit was supposed to return to life, to be born in a more noble warrior, until in the final stage a Krontep would become a king and, eventually, reach the home of the gods. (TV: Mindwarp)

After his encounter with The Book of the Old Time, the Seventh Doctor began to suspect that before regeneration, there had been reincarnation. (PROSE: Cat's Cradle: Time's Crucible) The Doctor later discovered that he might have been the genetic reincarnation of the Other. (PROSE: Lungbarrow)

The Vandosians used quantum runes to determine when and where a person was reincarnated. Through this, they believed that in 1979, Shogalath had returned in the body of the human, Phil Tyson. Under Vandosian law, a reincarnation was to be held accountable for the previous life's crimes. (COMIC: Mr Nobody)

The Great Intelligence is the ultimate result of an ascended soul which began as Gordon James Lethbridge-Stewart and through many reincarnations ended, thousands of years in the future, with Mahasamatman. The other reincarnations included Owain Vine and Adam Wicks. (PROSE: The Forgotten Son, Night of the Intelligence)

Other references
The Aja'ib contained tales involving reincarnation. (PROSE: Bafflement and Devotion)