TV Tropes has a definition of Word of God and examples of it here.
Word of God has an odd relationship with the canon of a work, but I think it can best be summed up as: Word of God is Canon if it agrees with you and Not Canon if it disagrees with you.
One of my favourite examples of Word of God is that, in Warhammer 40,000, the immortal God-Emperor of Mannykind is Cliff Richard.
I am now going to look at two examples of Word of God within Doctor Who. Doctor Who has lots of writers, as well as other mannys involved in making it such as producers and directors and actors, so it is harder to tell who would count as God for Word of God.
In an episode of Doctor Who Confidential, Russell T Davies said that the origins of the Time War go back to the Doctor being sent to Skaro to avert the Genesis of the Daleks. This is an example of Word of God, but it seems to me to be a rather arbitrary place to put the origin of the Time War. Why not say it goes back to The Chase, which is the first time we see that the Daleks have time machines of their own?
This is less a problem with Word of God than with trying to assign an origin to a Time War. Besides, if we wanted to disregard Russell T Davies as a source for Word of God-type authority, we need look no further than his statement on who would make a good Doctor:
"Hitler. He was stern and strong. He would be great."
To really see the limitations of Word of God, we can look at an example where the mannys in charge of Doctor Who at the time - producer, director and script-editor - intended for something to be canon in spite of it contradicting facts established both before and afterwards.
The Morbius Doctors
In the 1976 Doctor Who story The Brain of Morbius the Doctor (played by Tom Baker) fights the baddy Morbius in a mind-bending duel. We see Tom Baker's face, and then we see the faces of the three earlier Doctors - Jon Pertwee, Patrick Troghton and William Hartnell - appear in turn.
What happens after this is open to interpretation, and the Word of God interpretation runs directly contrary to the accepted Canon interpretation. We see eight more faces: are they the faces of Morbius, or of previously unseen regenerations of the Doctor?
Christopher Baker as either (a) Morbius, or (b) the Eighth Doctor
Robert Holmes as either (a) Morbius, or (b) the Seventh Doctor
Graeme Harper as either (a) Morbius, or (b) the Sixth Doctor
Douglas Camfield as either (a) Morbius, or (b) the Fifth Doctor
Philip Hinchcliffe as either (a) Morbius, or (b) the Fourth Doctor
Robert Banks Stewart as either (a) Morbius, or (b) the Third Doctor
George Gallaccio as either (a) Morbius, or (b) the Second Doctor
Christopher Barry as either (a) Morbius, or (b) the First Doctor
Evidence in favour of (a) Morbius
This is the version commonly accepted as the canonical one, because it is supported by virtually every piece of on-screen evidence within Doctor Who but external to The Brain of Morbius itself: the images must be those of Morbius because they cannot be those of the Doctor because William Hartnell played the First Doctor.
This had been established prior to The Brain of Morbius - in 1973's The Three Doctors William Hartnell's Doctor is referred to by the Time Lords as being the Doctor's "earliest incarnation" - and it would go on to be reinforced many times in later eras, right up to the present day.
Evidence in favour of (b) the Doctor
Here is where Word of God comes in - when they made the story, the production team intended for the faces to be those of the Doctor. The following passage is taken from A History of the Universe by Lance Parkin:
however much we might want to fit this scene into the continuity of the series as established elsewhere or rationalise it away, here, as the sequence of mysterious faces appears on the scanner, Morbius shouts "How far Doctor? How long have you lived? Your puny mind is powerless against the strength of Morbius! Back! Back to your beginning! Back!". These are certainly not the faces of Morbius, as has occasionally been suggested, or the Doctor's ancestors, or his family. Morbius is not deluding himself. The Doctor does not go on to win the fight, he almost dies, only surviving because of the Elixir, it just happens that Morbius's brain casing can't withstand the pressures either.
The production team at the time (who bear a remarkable resemblance to the earlier Doctors, probably because eight of them - Christopher Barry, George Gallacio, Robert Banks Stewart, Philip Hinchcliffe, Douglas Camfield, Graeme Harper, Robert Holmes and Chris Baker - posed for the photographs used in the sequence), definitely intended the faces to be those of earlier Doctors. Producer Philip Hinchcliffe said 'We tried to get famous actors for the faces of the Doctor. But because no one would volunteer, we had to use backroom boys. And it is true to say that I attempted to imply that William Hartnell was not the first Doctor'.
If you consider only the three seasons of Doctor Who produced by Philip Hinchcliffe then there is little, if anything, that contradicts this view. It is the rest of Doctor Who's 50 year run that seems to want to disprove Hinchcliffe's attempt at making himself the real Fourth Doctor.
Perhaps one of the main reasons there is no room for there to be extra Doctors before William Hartnell is that the number of regenerations the Doctor can have is limited and so there is a desire for them to be enumerated and thus become a known quantity.
However, the number of regenerations only became limited in a story the season after The Brian of Morbius. The Deadly Assassin, by Robert Holmes (our would-be Seventh Doctor above), confines Time Lords to twelve regenerations, or thirteen incarnations.
But Robert Holmes was also script editor - and heavily involved in the writing - of The Brain of Morbius. So taking these two stories together, along with the fact that Holmes could have picked just about any number for how many regenerations are allowed, and it seems that he wanted to suggest that Tom Baker was the Twelfth Doctor, and therefore must be the second-to-last Doctor.
Wait, it gets even better. If Tom Baker was the second-to-last Doctor, then that would mean Peter Davison was the final Doctor. And who wrote the final story for this final Doctor?
Robert Holmes did.
Consider the Doctor's dialogue just before the regeneration:
"Is this death?"And:
"I might regenerate; I don't know. Feels different this time."Does even the Doctor think he has now reached the end of his last life?
Also the regeneration itself (directed by Graeme "Sixth Doctor" Harper) looks very different from any of the Doctor's other regenerations. Why is that? Could it be..?