He is, as the Face of Boe has said, the lonely god, the wandering god. But he is not entirely alone. The Doctors may change, over the years, but the TARDIS remains, constancy in his chaotic life, the agent of chaos through which he creates stability.
For this is the true secret of the TARDIS: she is not broken at all, but a sentient being in symbiosis with the Doctor. He has an unparalleled urge to do good, to fix what is broken in the universe and get it all back on track, though he might not always know it, so she indulges him. He chooses a time and place to which he wants to go, and she finds the nearest point of trouble and takes him there. He may complain, and it may result in high Companion turnover, but he loves every minute of it. This is especially poignant with the Tenth Doctor, as he relearns his love of putting things right.
The Ninth Doctor needed Rose, needed someone who would just go along with him because it seemed like a good idea. He had made such terrible judgment calls, lost so much, he just needed someone who could show him the beauty and wonder of the universe again. The Tenth Doctor was a little more together, a little more willing to try his hand at changing things and interfering. Rose, however, was still trying to live as she had with Nine, bouncing around exploring more than actually changing things. This is why Martha was so good for Ten- she has such an impulse towards helping, herself, that she reawaked it in him. He began to actively seek ways to help once again.
The TARDIS, of course, always knows what the Doctor needs. She takes him to his Companions, each of whom is a perfect foil for the Doctor in some way (i.e. Rose could show him how to be happy again, Martha challenged him mentally). She helps him find what he really wants, which is a way to help. Even when all he wants is an escape, she finds a way for him to help someone, which in the end makes him feel better than a simple holiday would. More than all that, though, is an incident from the very end of Nine’s story.
The Doctor is seemingly doomed. He has sent Rose away, and locked the TARDIS so they don’t come back for him. In reverse order, Rose: saves the Doctor; leaves herself clues on how to do it in all the time/places they’ve traveled together; takes in the Time Vortex at the heart of the TARDIS (essentially becoming part of it); opens the Vortex; and finds/solves the clues. The TARDIS needs an agent, a being with arms and legs and eyes, in order to do what she wants. In this case, that means saving the Doctor, and incidentally herself, by switching her symbiosis from the Doctor to Rose for a little while. She could then bring them all back together, and fulfill Nine’s other greatest wish, to see the Daleks destroyed before his eyes.
This, by the way, is the reason Ten’s Regeneration is a little jumpy and uncertain: It is linked closely with the TARDIS herself, and she had recently expended a great deal of energy on dealing with Rose and the Daleks and all.
In the end, though the phrase “wandering god” most definitely applies, “lonely god” does not, quite. The Doctor and his TARDIS are as close as a happily-married couple, and it is truly a Pantheon of two.