The Doctor's species

Much like their age and their early life, the Doctor's species was a matter of much contention due in part to shifting timelines. (PROSE: Celestial Intervention - A Gallifreyan Noir)

The vast majority of sources agreed that the Doctor was a Gallifreyan and a Time Lord, (TV: The War Games, et al.) but a few suggested that they had different origins. Various accounts identified the Doctor as being fully or partially human, (PROSE: Doctor Who and the Daleks, TV: Doctor Who, et al.) having once been the Timeless Child from an unknown species, (TV: The Timeless Children) or as the product of still stranger origins. (PROSE: The Death of Art, Sometime Never..., et al.)

Time Lord

Although human-like in appearance and broad mannerisms, the Doctor was by most accounts not human; (PROSE: Who is Dr Who?) the Doctor usually identified themselves as a Time Lord (TV: The War Games, Pyramids of Mars, The Night of the Doctor, et al.) from the planet Gallifrey in the constellation of Kasterborous. (TV: The Day of the Doctor)

A previous life, a previous race

According to one account, however, the Doctor's childhood on Gallifrey with the Master was a result of their having been regressed into a child, and their memories redacted, after a large number of regenerations; they were originally the Timeless Child, a being of an unknown species whom the Shobogan explorer Tecteun adopted and brought back to Gallifrey, harnessing the Child's regenerative abilities to turn her people into the Time Lords. Though she sequenced her adopted child's entire DNA, Tecteun was still no closer to discovering the true origins of the Doctor. (TV: The Timeless Children)

In a similar but distinct account, the First Doctor was indeed the first incarnation of the Doctor as such, but was the reincarnation of the Other, one of the Founders of Gallifrey, whose mind and genetic structure had been redistributed into the Loom which created the Doctor many millennia later. (PROSE: Lungbarrow) According to The Thousand and Second Night, a highly figurative account of early Gallifreyan history, the Other was "neither an angel nor a djinn". (PROSE: Head of State)

Half-human?

The Eighth Doctor had vivid memories of his childhood on Gallifrey, but he also claimed that his mother was human; the Bruce Master's analysis of the Doctor's retinal structure seemingly confirmed that he was half-human, (TV: Doctor Who) although the Eighth Doctor would later claim that he had tricked "his greatest enemy" into thinking him to be half-human using a "half-broken Chameleon Arch". (COMIC: The Forgotten) While the Eighth Doctor was on Dreamstone Moon, Isabella Cleomides reported that his retinal structure instead denoted Partriscisnad origins. (PROSE: Dreamstone Moon)

The Eighth Doctor, when being interrogated about his origins, also once claimed that he was from Andromeda, his mother having been "abducted by little green men". (PROSE: Seeing I)

Human

By other accounts, the First Doctor and the Second Doctor were human beings (TV: The Evil of the Daleks, PROSE: Doctor Who and the Daleks, The Monsters from Earth) whose powers of renewal were a function of the TARDIS they piloted. (TV: The Power of the Daleks) The Daleks believed that it was as a result of his many travels through Time that the Doctor had become "more than human". (TV: The Evil of the Daleks)

One account referred to the Doctor as the greatest human mathematician, whose equations had at long last united Space and Time fully into the inextricable concept of the Idea of the Living Matter. This had allowed him to construct the TARDIS, a machine which could withstand and travel through Eternity and Infinity in a microsecond. (PROSE: The Equations of Dr Who)

Other possibilities

In the post-War universe where the Time Lords never existed, (PROSE: The Adventuress of Henrietta Street) the Doctor was originally a member of the Council of Eight named Soul, who lost his memory following a confrontation with the Eighth Doctor. (PROSE: Sometime Never...)

The Doctor occasionally appeared to his companions as something godlike or monstrous. Bernice Summerfield saw the Seventh Doctor as a transdimensional monster "crammed down into a parody of human flesh." (PROSE: Transit) Roz Forrester suggested that he matched the description of Nyarlathotep, (PROSE: The Death of Art) the darkest and greatest of the Old Ones. (PROSE: The Quantum Archangel)

Later developments

The Fifth Doctor allowed himself to become a vampire so he could stop Ruath's plan to resurrect Yarven. Following this, he changed himself back to normal. (PROSE: Goth Opera)