When Doctor gets to Trenzalore, "Silence" was supposed to fall.
In the Name of the Doctor I can name a few things that fell:
So since this episode is where the Doctor finally reaches Trenzalore -- What Silence fell?
We've been led to assume for quite some time that "Silence will fall" somehow refers to The Silence/Silents. But you're right, they did not fall in this episode.
I don't think we're done with Trenzalore. Not only did Silence not fall, but Dorium Maldovar's prediction of this all taking place "at the Fall of the Eleventh, where no living creature could speak falsely or fail to answer" has not happened yet either.
There would seem to be two occasions where this could still happen. Firstly, the episode ended on a cliffhanger, with the reveal of John Hurt, and everyone is still on Trenzalore. Secondly, although this might well be the same time, we haven't yet seen the events that lead to the Doctor actually dying on Trenzalore.
In my opinion, we'll see more of this on the 50th anniversary episode in November, and with some luck the Silence will reappear and - presumably - fall.
As explained in "The Wedding of River Song", the phrase "silence will fall when the Question is asked" should be translated as "silence must fall when The Question is asked," and, as explained in "Let's Kill Hitler", it is the core belief of the Silence. That is an important distinction; "silence must fall when the Question is asked" isn't a prophecy, it's the Silence's mission statement; the actual prophecy, in which there is no mention of "silence," is "on the fields of Trenzalore, at the fall of the eleventh, where no living creature can speak falsely or fail to answer, a Question will be asked; a Question that must never, ever be answered." The Silence believe that the Question must never be answered and that the Doctor must never be allowed to reach Trenzalore, so they are intent on killing him before he can get there. As the Doctor explains, the "silence" that must fall, according to the Silence, is his own - he must be dead by the time that the Question is answered. The Doctor explains to Churchill that if there was a man who knew a dangerous secret, and you wanted to erase that secret from the world before it could ever be spoken, you would kill him, and his silence would fall. If the person who knows the answer to the Question is dead, then when it is asked, it will be met with silence.
Since the Doctor managed to faked his death, his silence can no longer fall because he is still alive and is still capable of answering the Question. By the time he gets to Trenzalore, "silence must fall" will have no more relevance because the Silence will have failed in their mission to ensure the Doctor's silence.
To open the doors to the Doctor's tomb, his name must be said. The Silents didn't want anyone to be able to enter the tomb. They knew what someone could do by entering the Doctor's timestream, like the great intelligence eventually tried to do. The silence that they believed should fall, was when the great intelligence asked the Doctor's name in order to open the tomb. River said his name to open the tomb, the only ones who supposedly could hear her were the Doctor and Clara. Though we can assume Clara didn't hear her say his name. From everyone else's perspective silence fell when the question was asked, the question being what the Doctors name is.
There are reasons to suppose that the events set out in the Name of the Doctor episode are not a good fit with and do not fulfill the Silence prophecy. If that is so then the prophecy remains to be fulfilled in the Time of the Doctor special also set in Trenzalore, but at a time of war, which is more in keeping with the prophecy. This answer assumes the prophecy is still awaiting fulfillment on the fields of Trenzalore and the question has not yet been asked.
It is notable that the prophecy does not say who asks the question. Still, the line "Silence must fall when the question is asked" is frequently taken as a kind of scriptural justification of attempts to kill the doctor confirmed by several attempts on his life which are meant to make sure the Doctor is taken out of the picture (by being killed) and therefore never makes it to Trenzalore and never is in a position to answer the question.
That could be a valid reading of the prophecy but I think it is tortured and there is another available reading. There is the possibility that the Doctor asks the question at Trenzalore, a question that the prophecy says must "never ever be answered". Now for those faithful moved by Silence prophecies - Silents if you like - if they believe themselves justified to murder someone because "silence must fall when the question is asked" going so far as to even preempt events in the prophecies themselves would they not feel justified in murdering someone because they are the one who will ask the question that must never ever be answered (and surely will be answered if asked)? Bottom line is Silents appear to act automatically to try to bring about whatever it is that Silence prophecies say must happen.
At this point all attempts to preemptively nudge reality into conformance with the prophecy have failed. The Doctor is alive and well and it seems certain that events will unfold that to some degree parallel those set out in the prophecy. There is ample evidence that the Silents a) actively manipulate events to achieve certain ends b) that the ends are guided by the prophecies but c) if the ends can be fixed before matters come to a head in the form set out in the prophecies by pre-emtive actions to nudge things toward the given end, then these pre-emptive actions should be taken. Commonly, the Silents try to change still moments into fixed moments in time that fulfill their objectives. They take their guidance from the prophecies but are more wedded to the spirit than the letter of the prophecies. So, for example, making the Doctor's death at Lake Silencio a fixed moment is a way to ensure that the prophecy is fulfilled - that an answer to a question that should never be uttered is never uttered - without inviting the troubling uncertainty that arises when the one who will ask the question is allowed to get to Trenzalore.
The Silents appear to read the prophecies with an eye toward what they suggest. That may explain why they are not bothered by deviations from the letter of what is expressed there. It is reasonable to suppose that with their objectives as yet unfulfilled they will continue trying to ensure that "silence will fall" that is that the doctor is eliminated or killed or falls.
A major problem with the reading of the prophecy that I propose is that it is apparently absurd for the Doctor to ask of anyone else the question "Dr. Who?". But we know that this has been a question that the Doctor has been running from all of this life. So, if there are limits to the Doctor's self-knowledge or there are aspects of his identity or past that are opaque to him or that he has forgotten it makes sense that he should ask a question that could bring new clarity. For that to be the case there would need to be someone who could answer the question. And the answer would be what matters most. The whole prophecy storyline begins making some kind of sense if ultimately there is concern over what the Doctor learns when the question is answered. Someone or something is worried that the Doctor will be able to act on what is learned and that would be the reason why "silence must fall when the question is asked".
No 'silence' fell during that episode. The prophecy is about the battle that resulted in the graveyard we see in The Name of the Doctor. During that battle, Silence fell. The main reason I think this is the case, is because:
when no living creature may speak falsely or fail to give answer
wasn't really part of the events of that episode. The Doctor clearly failed to give an answer, River was the one who provided the answer.
We see the events of the prophesy play out in the recent Christmas Special episode, The Time of the Doctor. In it, The Doctor and Clara go to a world revealed to be Trenzalore. The crack from Series 5 is in a building on the planet, in a small town. It is emanating a 'truth field', which prevents people from 'speaking falsely' (see above prophecy). A signal is coming from the crack, which contains an encrypted message asking a question over and over:
Doctor Who?
They come to the planet, and find many ships from various races. Each race sent one ship to investigate the signal, which is being transmitted throughout time and space. The Church got there first. To protect the planet, they setup a shield to prevent anyone from going to the planet or attacking it. When the Doctor arrived, The Church sent him down to investigate.
The signal is coming from Gallifrey, outside the universe after the events of Day of the Doctor. If the Doctor speaks his name they'll return, but in so doing, will restart the Time War. Upon learning this, The Church dedicates themselves to Silence, the silence of the Doctor, as they do not want the Time War to return. As The Church's leader proclaims:
Silence must fall.
A repeating theme of the 11th Doctor's run, and something related to the prophecy, "Silence will fall when the Question is asked" (Let's Kill Hitler).
So The Church helps maintain a truce, they help the Doctor prevent any of the races from invading the planet, and he does not answer the question. Then time passes as they maintain the truce. Centuries pass, the Doctor grows old.
At the end of the episode, the Daleks break the truce and invade the planet. Clara argues into the crack that the Time Lords don't need to hear the Doctor's true name, they just need to help him. They do so by providing him with a new set of regenerations. The 11th Doctor dies of old age, blasting the Daleks with his regeneration energy, saving the planet as his regeneration begins.
And so the Eleventh falls. This fulfills the prophecy, and explains, "what Silence?" It's the Doctor's silence; his refusal to answer the question. This gets copied into Church faith, which ends up being the source of the past events where the Silence try to kill the Doctor.
Largely copied from my answer over on Movies & TV.SE
The doctors silence of his secret, that is the Doctor with no name, the one who is not allowed to hold the doctors name, as he broke the promise that the name encompasses - the promise to protect I presume
