The Doctor has lived a long life. He's lived so long and had many faces. His face, his clothes, his companions, they all change, but not what he carries. With him always is the faithful sonic screwdriver. The deceptive psychic paper. And the ever important TARDIS key. He could carry more, his pockets are bigger on the inside after all, but that's all he can carry.
The sonic has always been a blessing more than burden. It's gotten him out of many harrowing situations. It's locked the TARDIS coordinates, preventing the Master from escaping for one. He's improved mobiles with it. The companions always like that. Universal roaming with incredible reception that even lets them phone home when they need. It's a reassuring weight in his pocket. Tells him he'll always be okay. That he can always get away.
His psychic paper which rests in his breast pocket of his coat. Now there's a terribly wonderful thing to carry. Rule One: The Doctor lies. It's easy with psychic paper. He can be anyone, but The Doctor. He can be a home inspector, a school caretaker, even the unassuming John Smith. It's a reminder of what he really is. A liar. He's lied to those he loves. He's lied to trick his enemies to their death. All he does is lie. He's forgotten his own name because of it at times. Becoming unrecognizable to his own eyes that he has to ask: "Am I a good man?"
The key he carries is always on him. It has to be otherwise he's lost. It's a reminder. A reminder that he has a home. A reminder to return, to find it. He's been on that path for centuries. It's been so long, but he likes to think he's on his way home, the long way round.