Fanon
Fanon is a body of popular suppositions and theories accepted by fans concerning the Doctor Who Universe. It is a portmanteau of the words "fan" and "canon".
Fanon often gets confused for "canon", even if it is not supported by evidence either on screen or in print.
Derivations
Some fanon derives from from non-canon sources such as The Doctor Who Role Playing Game, which, for example, made the Master, the Monk and the War Chief into the same Time Lord.
When stories break fanon conventions, it can cause controversy. A longstanding piece of fanon is the supposition that the Doctor, due to his alien nature, is incapable of romance or sexual attraction. Despite the existence of a granddaughter, and occasional minor references during the early years of the show, much of this supposition stems from the Fourth Doctor's odd reference to Countess Scarlioni in DW: City of Death as "a beautiful woman, probably," as well as the 1963-89 series' general aversion to including romantic entanglements due to its long-standing image as a children's program. The Doctor Who telefilm of 1996 was controversial with some fans because it showed the Eighth Doctor kissing Grace Holloway twice, the latter in an unambiguously romantic way, which was accused of violating canon, even though it only violated fanon. (The revived series has since thoroughly rendered this piece of fanon moot by featuring later Doctors in numerous romantic situations and entanglements; several novels published since 1991 have also featured romantic situations for the Doctor previously considered taboo; examples include Human Nature and the conclusion of The Dying Days.)
An example of fanon stemming from the series revival is the question of "TARDIS coral". Fans have come to use this term to refer to pieces of TARDIS obtained by Jack Harkness (Torchwood) and the Meta-Crisis Tenth Doctor (DW: Journey's End - deleted scene). In fact, as of July 2009 no episode has ever used the term to describe these objects, nor have any close-ups indicated whether they are, indeed, coral-like. The issue is further muddied by the fact the Journey's End reference was deleted from the final episode, raising the question of its canonicity.
When fanon becomes canon
Fanon and canon are not necessarily exclusive of each other. It has been occasionally known for elements originating in fanon to be adopted into canon.
In Spin-offs
The BBC has never made a firm proclamation regarding whether novels and other spin-off works should be considered canonical in relation to theier television series. Still, spin-off media have been known to add elements of fanon into their own canon.
Some fan theories, such as the Season 6B theory, while not as yet confirmed on-screen, have been supported by expanded universe spin-offs such as novels (which are of uncertain canonicity). Others, such as the question raised by DW: Planet of Fire as to whether the Doctor and the Master are actually brothers, have been denied by off-screen sources, if not necessarily on-screen.
The aforementioned Season 6B theory comes close to being "canon", having been featured in a BBC Past Doctor Adventures novel and endorsed by former script editor Terrance Dicks (who wrote the book in question, World Game). This theory started with a series of 1969 TV Comic stories featuring a companion-less Second Doctor exiled on Earth (and, after a few adventures, being forced to regenerate inside his TARDIS), and continued with his involvement in both DW: The Five Doctors and DW: The Two Doctors.
In Televised Doctor Who
Occasionally, a piece of fanon will find its way not just into the spinoffs, but into Doctor Who proper.
- The concept that the Doctor's TARDIS is meant to be operated by six pilots at once was a long-standing piece of fanon which was finally confirmed in Journey's End.
- The idea of the Doctor's TARDIS being a sentient, living creature in its own right rather than a mere functional vehicle was occasionally distantly implied in the classic Doctor Who television series, but greatly expanded upon in fanon and spin-off media. Eventually the concept found its way into televised Doctor Who, with the Ninth Doctor declaring the TARDIS to be "alive" in Boom Town, and the soul of the TARDIS making itself fully known to the Eleventh Doctor in The Doctor's Wife.
- The concept of Time Lords being able to change gender when they regenerate was hinted at by the original production team - most notably when John Nathan-Turner and Tom Baker hinted that his replacement in the role of The Doctor might be female - but never used on-screen. The idea entered fanon and occasionally appeared in spinoff media such as Exile before eventually being mentioned on-screen in The Doctor's Wife.