The final reward Edit
After returning the Time Lords and Gallifrey to the end of the Last Great Time War and their deaths, the Doctor realised he had survived. Then he heard four knocks. Wilf was trapped inside a radiation control booth, about to be flooded with radiation. Despite his anger and Wilf's pleas to leave him, he released Wilf and took his place, receiving a fatal dose of radiation.
At first it appeared the Doctor had survived this, but when a wound on his face suddenly healed itself, the Doctor realised that the regenerative process had begun. Unlike previous occasions, the actual regeneration did not immediately occur and the Doctor was able to return Wilf to his home and spend an unknown length of time travelling through time and space, revisiting his past companions, an act he referred to as his "reward". (TV: The End of Time)
The reward Edit
He went to 13 Bannerman Road where he saved Luke Smith from being run over by a car. Luke rushed to his house to tell his mother, Sarah Jane, of his appearance. She went outside and called out to the Doctor, who acknowledged her, but did not reply, but entered his TARDIS. Sarah Jane seemed to know what was going to happen, but was still glad to see him.
He travelled to a bar, where Captain Jack Harkness was drowning his sorrows in a drink. He passed a note to Jack reading, "His name is Alonso". Jack turned to see Midshipman Alonso Frame and the Doctor departed, after He and Jack saluted one and other, as the two began flirting. (TV: The End of Time)
The Doctor entered a bookstore where Verity Newman, a descendant of Joan Redfern, was signing copies of her book, A Journal of Impossible Things, which was the journal the Doctor had written as John Smith. (TV: Human Nature, The End of Time) The Doctor had Verity sign his copy, and she realised who he was. The Doctor asked Verity if Joan had been happy in the end which she confirmed, but he refused to answer her question of if he was.
He encountered Geoff Noble at some moment before the man's death, and borrowed a pound from him. He went to the future and used that pound to purchase a winning lottery ticket. He arrived at the wedding of Donna Noble and Shaun Temple, and asked Sylvia Noble and Wilf to give Donna the triple rollover-winning ticket as a wedding gift. (TV: The End of Time)
The Eleventh Doctor would reveal to Sarah Jane and Jo Jones that he visited all of his former companions from all of his previous incarnations, seeing how they got on. He found that Jo had twelve grandchildren with a thirteenth grandchild on the way, and that the child would be dyslexic, but a good swimmer. (TV: Death of the Doctor)
Finally, he went to the Powell Estate on 1 January 2005, where he observed Rose Tyler and her mother, Jackie Tyler, months before Rose first met him, in his previous incarnation. Although he kept to the shadows, a sudden spasm of pain caught Rose's attention and the two exchanged New Year's greetings. The Doctor told Rose that she would have a "really great year" with tears in his eyes.
After Rose departed, the pain of regeneration overwhelmed him and the Doctor collapsed in the street. Ood Sigma appeared and told him that while his song was ending, his story never would, and the universe would sing for him.
Reaching the TARDIS, he piloted it into orbit around Earth, said "I don't want to go" and regenerated into the Eleventh Doctor. The energy released during the regeneration caused massive damage to the TARDIS. (TV: The End of Time)