Ninth Doctor's regeneration

The Ninth Doctor met his regeneration into the Tenth Doctor as a result of absorbing the energy of the Time Vortex to save the life of Rose Tyler. (TV: The Parting of the Ways) By later accounts, this was the tenth regeneration of the 12-regeneration life cycle beginning with the First Doctor; as the Eleventh Doctor remembered, the so-called Ninth Doctor followed the true ninth incarnation, who did not identify as the Doctor. (TV: The Time of the Doctor)

Causes
At the end of the Battle of the Game Station, Rose Tyler absorbed the Heart of the TARDIS and became Bad Wolf. Knowing that Rose would burn up if she kept so much power in her body, the Doctor drew the Time Vortex from her body and into his own with a kiss, before sending it back into the heart of the TARDIS. He then took an unconscious Rose into the TARDIS, abandoning a resurrected Jack on the deserted Game Station.

Knowing that his possession of the vortex energy had caused cellular damage to his body, (TV: The Parting of the Ways) the Doctor looked back on his life, deciding what was "fantastic", and that it "meant a lot". (PROSE: Shortness of Breath) He told Rose how he had wanted to take her to "so many places", such as the planet Barcelona. Trying his best to explain that he was about to regenerate, the Doctor told Rose that they had both been "fantastic", and then regenerated into his next incarnation. (TV: The Parting of the Ways)

Regeneration
The regeneration was a quick explosion of golden energy. (TV: The Parting of the Ways)

Aftermath
After regenerating, the new Doctor noted his new teeth, and intended to take Rose to the planet Barcelona. (TV: The Parting of the Ways) But with Rose suffering an emotional crisis over his sudden change, he instead decided to take her home to the Powell Estate in London. En route, he convinced her of his identity by reminding her of the first word the Ninth Doctor had said to her, before beginning to suffer adverse effects from his regeneration. Experiencing manic hyperactivity, he accelerated the TARDIS' speed. (TV: Born Again) Crash-landing the TARDIS at the Powell Estate on Christmas Eve 2006, the Doctor fell into a coma after wishing Jackie Tyler and Mickey Smith a "Merry Christmas".

The Doctor slept through much of the ongoing invasion by the Sycorax. When the TARDIS was taken aboard a Sycorax spaceship on Christmas morning, he finally awoke with the help of some tea that seeped into a component of the TARDIS, (TV: The Christmas Invasion) alongside regeneration energy which he seeped from his third incarnation, who had arrived in Jackie's apartment moments before. (PROSE: The Christmas Inversion) Stopping the Sycorax leader's blood control of humanity, the Doctor challenged him to a duel over the fate of Earth. In the ensuing sword fight, the Sycorax leader chopped off the Doctor's hand. However, because he was still within the first fifteen hours of his regeneration cycle, he grew a new hand and went on to win the duel. (TV: The Christmas Invasion)

The Doctor's severed hand was recovered by Jack Harkness (TV: Day One) and eventually reclaimed by the Doctor after being exploited by the Saxon Master during the Toclafane invasion. (TV: The Sound of Drums/Last of the Time Lords) Ultimately, the hand was used by the Doctor to prevent himself from changing when a Dalek forced his eleventh regeneration during the Planetary Relocation Incident. Soon after, a Human-Time Lord Meta-Crisis occurred, transforming the hand into the Meta-Crisis Doctor and Donna Noble into the DoctorDonna. (TV: The Stolen Earth/Journey's End)