The Tenth Doctor
In saving Rose Tyler, the Doctor was heavily injured, and dieing. The Doctor then regenerated into this form. When he regenerated, Rose didn't believe this to be the Doctor. The Doctor convinces her by reminding her of what he said to her when they first met. She then believes him to be the Doctor. He then starts running around the TARDIS, and starts pulling random levers. She tells him to stop, he doesn't listen. He just rambles, and makes the TARDIS go faster and faster (he appears to be going insane). They start heading towards London, Christmas Eve.
The TARDIS appeared in London. The TARDIS actually crash landed (it hit many buildings and a few parked trucks on the way down). The Doctor stepped out to meet Mickey Smith and Jackie Tyler. He kept rambling and rambling to them both until finally saying "Merry Christmas!" and collapsing. When rose stepped out of the TARDIS, Rose confirmed him to be the Doctor - to which Jackie replied "Doctor who?"
The Tenth Doctor has the same powers as all Time Lords. The Doctor's brain can handle and understand more information then most other species. The Doctor also has two hearts. The Doctor's senses are also very high.
The Doctor can survive much high levels of radiation then a human could.
He has a much higher stamina then that of a human.
The Doctor can regenerate at will. When wounded and about to die, he will do this. Regeneration will change his body, and even his personality. Yet, he will still remember his past, and is still the same person. This is The Doctor's tenth regeneration.
The Doctor is one of the most intelligent beings in the universe. He is able to identify almost any species by a simple description, he even knows their home planet. He is intelligent enough to know even the genetic codes of beings, and how almost any type of machine works. He knows almost everything that has ever happened in history anywhere.
Doctor Who series 1 (season 27):
Doctor Who series 1/2 (season 27/28) mini episode: "Children in Need Special"
Doctor Who series 2 (season 28):
Doctor Who series 3 (season 29):
Doctor Who series 3/4 (season 29/30) mini episode: "Time Crash"
Doctor Who series 4 (season 30):
"Voyage of the Damned"