Chameleon circuit

The chameleon circuit enables the outer plasmic shell of a TARDIS to assume any shape, in order to blend in with its surroundings.

General uses
A TARDIS with a functioning chameleon circuit can appear as almost anything, if its owner desires. The owner can program the circuit to make it assume a specific shape or else the TARDIS itself can decide what form to take. The chameleon circuit should make the TARDIS fit in to the natural environment of a specific destination. The perception filter also helps a TARDIS to disguise itself. (TW: Everything Changes)

The Doctor once referred to chameleon circuit of his TARDIS as a "cloaking device". The fact that he hesitated slightly before using the term "cloaking device" suggests that he was trying to think of an alternative to "chameleon circuit". (DW: Doctor Who: The TV Movie)

History
The chameleon circuit of the Doctor's TARDIS, however, has rarely worked properly since the First Doctor made a sudden departure from Totter's Lane, Shoreditch, 1963, and has usually remained in the shape of a London police box. (DW: An Unearthly Child)

The Doctor hoped to repair it in Logopolis by using Block Transfer Computations when  the Master interfered with the Logopolitans' calculations. (DW: Logopolis) He succeeded in repairing it for a brief period when he returned to Totter's Lane in 1986, but it quickly reverted to its usual police box form. (DW: Attack of the Cybermen)

During his seventh incarnation, the Doctor briefly enabled his ship to work again. (NA: The Left-Handed Hummingbird)

After Donna Noble reported her encounter with Rose Tyler to the the Doctor, he began noticing that the words "Bad Wolf" had begun to appear everywhere including replacing the traditional police box lettering on his TARDIS. These words were also visible from the interior of the TARDIS, over the doorway. It is likely the chameleon circuit was somehow activated in order to make this change. (DW: Turn Left).

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

However, the Doctor in recent incarnations has shown no particular interest in repairing the circuit, with the ninth incarnation more or less telling Rose that he likes its appearance. (DW: Rose) When the Master took possession of the TARDIS for an extended period of time, he also declined to fix the chameleon circuit. (DW: The Sound of Drums/Last of the Time Lords)

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. (DW: The Daleks' Master Plan)

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

The Master's TARDIS

 * A horse box (DW: Terror of the Autons),
 * A Computer bank (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 is in the shape of a red double decker bus (Number 22 to Putney Common), and is (at one point according to Iris) 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
Fanon has suggested that when the Doctor "borrowed" his TARDIS from Gallifrey, it was in for repairs, and one of the broken systems was the chameleon circuit.

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.''