Weeping Angels are one of the new Doctor Who villains, joining the ranks of Cybermen, Daleks, and Sontarans. They first appeared in the episode Blink, and have made several appearances since, including the final episode of the Rory/Amy Pond companions.
These creatures were created by Stephen Moffett, and they are a rather clever adversary for the Doctor. When nobody is looking at them, they can move about swiftly and quietly. Once someone looks at them, including another Weeping Angel, they become "quantum locked", where they appear to be made of stone. It's their natural defense against their enemies, and their race is almost as old as the universe.
The Angels also have an interesting method of taking someone over. If someone watches a video of an angel, the angel can get into someone's optic nerve and gestate, theoretically turning that person either into an angel or killing them.
To feed, the Angels will snag someone and throw them back in time, consuming the life energy they would have used from that moment up until they would have died. In Blink, this happens to several characters, and it creates an interesting question—what if someone they threw back completely changed things by "discovering" something, such as electronics? What if they happened to do a Marty McFly and have the stock market info or sports scores in their pocket? So far, these have not been covered.
My wife, who is not an avid watcher of the good Doctor, says they are the only really creepy and dangerous characters on the show. Sometimes, I have to agree.