The Silence are an alien race and religious cult that were featured in Doctor Who. They were most integral to the plot arc of Series 6, where they worked as powerful and mysterious antagonists for The Doctor. There will be major plot spoilers in this entry, so if you have yet to see Series 6, you may want to cease reading.
The Silence are tall, thin, faceless and androgynous aliens who resemble the painting The Scream. Their most fearsome and novel power is that they are memory proof: someone who interacts with one, even at length, immediately forgets them as soon as they lose visual contact. This has led to some truly eerie moments, as often the audience, like the characters, is not shown the presence of the Silence. We are often only shown the outcome of an encounter with The Silence: tally marks written on someone's skin so that they can remember that they had some type of encounter, although they won't remember what it was.
Along with their memory proofing, they also have the power to give post-hypnotic suggestions, as well as the more mundane ability to shoot lightning bolts. In the episodes The Impossible Astronaut/Day of the Moon, it was said that they were part of a conspiracy that had ruled the world for thousands of years.
All of which was discarded with The Time of the Doctor, where the once mysterious and sinister, and very powerful Silence were revealed to be only a splinter group of another religious groups, well-intentioned extremists. In fact, the Silence were originally engineered to be confessors, priests who could give absolution but leave people with no memory of the encounter. And who can shoot lightning. None of which makes sense, and is an example of how the writer of Doctor Who, Steven Moffat, has let down some of his promise. While a spectacular idea, the final resolution of the mystery of The Silence was very disappointing.