"A Christmas Carol" is the 2010 Doctor Who Christmas Special, starring Matt Smith as The Eleventh Doctor, Karen Gillam as Amy Pond, Arthur Darvill as Rory Williams, Michael Gambon as Kazran Sardick, and Katherine Jenkins as Abigail. It was written by Steven Moffat, although as the title suggests, it is based off of Charles Dickens' work.
The adaptation of "A Christmas Carol" for any television show that needs a stock plot for a Christmas episode is a well-worn tradition. It is such a cliché that it has come out the other end of cliché. And Doctor Who is certainly not a show that shies away from the corny.
The specifics of this plot are that Amy and Rory, after the events of The Big Bang, are on their honeymoon on a galaxy class starship, that falls into distress. It tries to land on a near-by planet, but the planet's weather is controlled by the Scrooge character, via a machine that is tied to his brain patterns. And he refuses to help. Luckily, The Doctor is there to reform him. He does this by going back in his past, meeting the young Kazran, and trying to teach him some humanity. In the present, the older Kazran's memories are changed at the same time as these events happen in the past. The young Kazran also falls in love with a poor woman, Abigail. He is almost saved, but when he finds that Abigail is suffering from a terrible sickness, his heart is broken. But this being a Doctor Who story and a Christmas special, the story eventually ends on a happy, if bittersweet, note.
This is a fun story, and perhaps my favorite Doctor Who Christmas Special. It is sweet without being too treacly, and the otherwise predictable plot is leavened with some odd weirdness and clever jokes. Not every Christmas Carol adaptation has Frank Sinatra, Marilyn Monroe, or a flying shark. And despite the ease and watchability, the show has some symbolic links to the upcoming epic of Series 6.