"The Next Doctor" was the 2008 Christmas Special of Doctor Who, starring David Tennant as The Tenth Doctor, David Morrissey as the titular "Next Doctor" and Velile Tshabalala as companion Rosita Farisi. The special was the first one that would kick off the run of Doctor Who specials over the next two years. It was written by series producer and showrunner Russel T. Davies.
As always, there will be spoilers with this encapsulation.
After the events of Journey's End, The Doctor finds himself in Victorian London. He seems peaceful and happy, which lasts all of three minutes before he hears a voice calling out "Doctor". As always he runs towards trouble, only to find someone else has gotten their first: a man who he finds out claims that he is The Doctor. At first, The Doctor thinks that he has met one of his future incarnations, who has already found a companion in Rosita. Who he takes to be his future self says that he has had most of his memories damaged during a war with Cybermen. The Doctor soon realizes that this is an unlikely story: for one thing, the Next Doctor's sonic screwdriver is a common screwdriver, while his TARDIS is a hot air balloon. Instead, the man who thinks he is The Doctor is a normal human who had a Cyberman "infostamp" (a form of data storage) blow up, sending all its information into his head and making him think that he was The Doctor. But as the Doctor points out to him, the courage he had was his own, even with an assumed identity. The Doctor and "The Next Doctor" join forces to destroy the Cybermen, an evil orphanage director, and a gigantic steampunk mecha rampaging across Victorian London.
This is a good special. It has a mixture of adventure, humor and drama. The interaction between David Tennant and David Morrissey, both excellent scenery chewers, is great fun to watch. Whether this show's deeper message about identity and self-knowledge goes along with its adventure and humor is probably a matter of taste.
Although this was the first of the specials, and was a good adventure in its own right, it would not yet touch on the arc that would run through the specials, ending in The Doctor's regeneration in The End of Time.