Even in the realms of fantasy and sic-fi, there are only so many people like him. Some characters have some of his traits, but few have all.
He is the wanderer, the the great one who is doomed to walk forever across the world without stopping for himself. He brings chaos in his wake, but he also rescues so many, saves so many, and keeps even greater negative forces at bay. He walks alone, in the end; yet he also makes friends along the way, friends who begin to understand who he is even if they can only share in part of his adventures. He can fit himself into any situation in any place: he can be regal or rustic, show off his intelligence or feign dim-wittedness, whatever is necessary. He usually thinks he is always right because he usually is right--but because he is so often right and so often great, when he falls he falls all the harder. Yet he can fall right into death and still return to the land of the living.
He is the Grey Pilgrim, Mithrandir; he is Gandalf. He is the Doctor.
Think about it. There are other characters who are outsiders, who pass by just long enough to save a few lives or the town or whatever it may be. There are characters who can be both serious and jolly. But what other characters share so many traits as Gandalf and the Doctor do? I have to keep pondering this: I really can't think of any more.
It is true that Gandalf is not the only wizard in Middle-earth. But the blue wizards are hardly spoken of, Radagast only makes a brief appearance (ha, ha, ha, Sylvester McCoy, who is the wizard doctor), and even Saruman becomes separate from Gandalf when he turns to evil. Saruman can also be like the Master. The Doctor wasn't always alone--and then, later, he finds that he is alone except for the Master, who always has so many evil plans. But perhaps the Doctor has more sentiment than Gandalf does. Gandalf's interest in hobbits is not so unlike the Doctor's interest in his companions, yet the Doctor always feels he has a connection to the Master just because they are all that's left of the Time Lords. Gandalf has no such loyalty to Saruman; he is only interested in keeping Middle-earth safe.
Wow, Doctor Who has really reawakened my character comparisons. But I think it says something that the comparisons are often of very valuable or well-crafted stories. If a story has powerful characters, that story will stick around, as both Doctor Who and The Lord of the Rings have done. These two characters have remained so memorable because they give us hope, not just the hope that the world can be made better but also the hope of living a simple day and enjoying it just for being itself.