Shapeshifter

A shapeshifter was a life-form possessing the ability to alter its physical form. (COMIC: The Shape Shifter)

Frobisher, the Whifferdill companion of the Sixth and Seventh Doctors, frequently used his species' shapeshifting abilities on their travels. (COMIC: A Cold Day in Hell!, Frobisher's Story, Changes) Frobisher fell ill with mono-morphia, which took away his ability to shift, leaving him stuck in the form of a penguin. (COMIC: Genesis!) He recovered enough to shift into various forms while battling another shapeshifter, a Kymbra Chimera, aboard the Doctor's TARDIS. (COMIC: Changes) After leaving the Doctor, they met again when the Time Lord was in his eighth incarnation. However, as Frobisher had taken a humanoid form and was known as Bish, and the Doctor had regenerated, neither recognised the other. (COMIC: Where Nobody Knows Your Name)

Another shapeshifter, the Brancheerian Decky Flamboon, was a companion of the Eleventh Doctor. Like others of his species, he could turn into almost anything. (COMIC: Meteorite Meeting)

The Aubertides were shapeshifters which could assume the appearance of anything they ate. (PROSE: Human Nature)

Axons could take the form of golden humanoids, although their real form was that of creatures that seemed made up of many tentacles. (TV: The Claws of Axos)

The Carrionites could take the form of beautiful women or ugly hags, although their real form was more bird-like. (TV: The Shakespeare Code)

The Gizou were shapeshifters which could change their size and shape through the use of proteus particles found in their body. (COMIC: Agent Provocateur)

The Gwanzulum took the form of individuals from other people's memories through telepathy, then fed on their life force. (COMIC: Planet of the Dead)

The Kymbra Chimeras were shapeshifters similar in abilities to the Whifferdill. (COMIC: Changes)

Multi-forms were shapeshifters which could change their shape by establishing a psychic link with another being and reading their minds though it took time to form the links, and when the form was assumed the other living being would collapse into a coma.

If a multi-form had to shapeshift with one form with another living creature, such as a dog, then it could become confused and the more complex life form could start to bark. This happened with Prisoner Zero who had problems taking on forms with more than one aspect, and the creature even lamented about it's problem. (TV: The Eleventh Hour)

Nostrovites were carnivorous shapeshifters. A number of them used their abilities to infiltrate the wedding of Gwen Cooper and Rhys Williams in order to extract an unborn Nostrovite from Gwen's womb. (TV: Something Borrowed)

Zygons were shapeshifters which required body-prints to assume another individual's form. It was necessary for them to activate their body-print regularly otherwise the pattern died and it couldn't be used again. (TV: Terror of the Zygons, The Day of the Doctor)

Members of the Rutan Host could use a metamorphosis technique to shapeshift into other forms, but they needed to know the form very well, usually after careful study and dissection. On Fang Rock in the 1900s, a Rutan killed Ben Travers to learn human physiology, enabling it to later take the shape of Reuben. When it transformed between shapes, it would glow green and would either shrink and compress down to size or grow to take on a humanoid form. (TV: Horror of Fang Rock)

Vespiforms could change into other species which were biologically compatible with the mimicked species. (TV: The Unicorn and the Wasp)

The Yend gained the ability to shapeshift after exposure to radiation from the rogue star Mortain. However, they were unable to control their transformations or stay in one form for long periods. (PROSE: The Sons of the Crab)

Another, rarely used term for shapeshifters was metamorph. Roz Forrester once shot and killed a metamorph which had taken her own form. (PROSE: The Also People) Bernice Summerfield guessed that Jason Kane was an empathic metamorph which had taken human form. (PROSE: Death and Diplomacy) AKA the Metamorph was an incarnation of I.M. Foreman which constantly shifted forms. (PROSE: Interference - Book One, Interference - Book Two) The Sixth Doctor once described Lampreys as "temporal metamorph[s]". (PROSE: Spiral Scratch)

River Song once dated a shapeshifter. She found them "tricky". (PROSE: The Day of the Doctor)

Butler and Swarf were shapechanger criminals. They could only transform for short periods of time. (PROSE: The Pit)