Chameleon circuit

The chameleon circuit was a component of a TARDIS which enabled its outer plasmic shell to assume any shape, in order to blend in with its surroundings.

Background
By default, TARDIS exteriors looked like plain, grey cabinets which opened via a sliding door. (DW: The War Games)

A TARDIS with a functioning chameleon circuit could appear as almost anything, if its owner so desired. The owner would be able to programme the circuit to make it assume a specific shape, or else the TARDIS itself could decide what form to take. The chameleon circuit would then ideally make the TARDIS fit in to the natural environment of a specific destination.

Flaw discovered
Prior to the Doctor's sudden departure from Totter's Lane, Shoreditch in 1963, the chameleon circuit of the Doctor's TARDIS worked perfectly well. (DW: An Unearthly Child) It was known to have taken the form of a large boulder on the planet Iwa, for instance. (TN: Frayed)

After the initial journeys of Ian Chesterton and Barbara Wright, however, the TARDIS remained fixed in the shape of a London police box. Neither Susan or her grandfather could explain why the ship had lost its ability to disguise itself.

Following this initial breakage, the Doctor failed to show much interest in repairing it. By the time of his ninth incarnation, for instance, he intimated to Rose that he simply liked its appearance. (DW: Boom Town) Other Time Lords who encountered the Doctor's TARDIS didn't seem to want to repair it, either. When the Master tried to repair the Doctor's Earthbound TARDIS, he expressed no particular concern with the fixing the chameleon circuit. (DW: The Claws of Axos). Much later, another incarnation of the Master took possession of the TARDIS for an extended period of time, but made no effor to fix the chameleon circuit. (DW: The Sound of Drums / Last of the Time Lords)

Repair attempts
Despite a general lack of enthusiasm for fixing the chameleon circuit, there were nevertheless a few restoration efforts.

The Doctor hoped to repair it in Logopolis by using Block Transfer Computations when the Master interfered with the Logopolitans' calculations. (DW: Logopolis)

Nyssa later tried to repair it on her own, without even referencing the TARDIS manual. After double-checking her work and finding it surprisingly sound, the Doctor chose an overly-ambitious environment for the first test of Nyssa's work. He materialized in one of Earth's oceans, whereupon it turned into a whale. It became so comfortable in its new form that it seemed to forget that it was a TARDIS at all. Only by transmitting his heartsbeat underwater and reminding it of its link to him was the Doctor able to swim into one of its arteries, undo Nyssa's fixes, and return it to its traditional police box shape. (BFA: The Deep)

The Doctor's next attempt was more successful. He repaired it for a brief period when he returned to Totter's Lane in 1986, but after it began to transform into shapes that still refused to blend into their surroundings - and on some occasions even made it hard to figure out how he was meant to enter his ship in the first place - he reverted it back to its usual police box form. (DW: Attack of the Cybermen)

During his seventh incarnation, the Doctor briefly enabled his ship — or, more precisely, a version of his TARDIS that he had acquired from an alternate time like where his third self had been murdered (NA: Blood Heat) —to work again. (NA: Conundrum) He later reset it to a police box after Mortimus hacked into the circuit and nearly gave away its location by turning it into the Statue of Liberty while he was materialised around Nelson's Column. (NA: No Future)

Later, when Donna briefly had a Time Lord consciousness, she began to tell the Doctor how to repair the circuit, but her brain began to overload before she could complete the instructions. (DW: Journey's End)

Despite the chameleon circuit being broken, the TARDIS occasionally still changed its basic shape. Though keeping the form of a police box, it would change the overall exterior height, shade of blue, the window panes and the text which appeared on the box. (DW: The Eleventh Hour et al)

The Monk's TARDIS
The Monk's TARDIS appeared as a sarcophagus in an English church of 1066, (DW: The Time Meddler), a large stone on Tigus, and a stone block in Ancient Egypt. The Doctor caused it to appear as an Ionic column, a stage coach, a tree, an igloo, a rocket, and a bi-plane before impishly setting it as a police box to distract the Daleks. (DW: The Daleks' Master Plan)

In 1976 London it assumed the form of a wooden desk. (NA: No Future)

The Master's TARDIS
The TARDIS belonging to the Master took on several different forms during his many encounters with the Doctor. These included:
 * A horse box (DW: Terror of the Autons),
 * A bank of computers(DW: The Time Monster),
 * A Corinthian column (DW: The Time Monster, Logopolis, Time-Flight),
 * A grandfather clock (DW: The Deadly Assassin, The Keeper of Traken),
 * The calcified Melkur (DW: The Keeper of Traken),
 * A police box identical to the Doctor's TARDIS (DW: Logopolis),
 * A fireplace (DW: Castrovalva),
 * The Concorde (DW: Time-Flight)
 * An "iron maiden" (DW: The King's Demons)
 * A space battle cruiser (Birth of a Renegade)

Others
The Rani's TARDIS took the form of both a cabinet (DW: The Mark of the Rani) and a translucent pyramid (DW: Time and the Rani).

Iris Wildthyme's TARDIS took the shape of a red double decker bus (Number 22 to Putney Common), and at one point, according to Iris, was slightly smaller inside than out. (EDA: The Scarlet Empress, The Blue Angel, Mad Dogs and Englishmen, PDA: Verdigris)

The TARDIS of Professor Chronotis looked like his rooms at St. Cedd's College. (DW: Shada)

Behind the scenes

 * The Chameleon circuit was originally referred to as a "camouflage unit". (DW: The Time Meddler). The next time the device was mentioned, its name was changed to "Chameleon circuit". (DW: Logopolis)
 * The real world reason for the malfunction is thought to be of a far more practical nature: the Chameleon Circuit was intended to allow the TARDIS to blend with its surroundings during the 'historical' episodes which would require an expensive redress of the TARDIS prop for every episode. Others have suggested that the shape was initially selected to provide something that the present audiences would instantly recognise.