This springs from a conversation Tim and I had on the long ride back from my parents' house yesterday afternoon/evening.
1. They both like cool hats - floppy wizard hats, fezes, Stetsons.
2. Gandalf could easily take care of the Weeping Angels. His staff and Glamdring broke the Bridge of Khazad-dum, and smote the Balrog. Obviously stone enemies, not a problem.
3. The Doctor could have sonic'd the door to the Moria open in Fellowship of the Ring.
4. The Doctor could have easily taken care of the whole Ring problem. He could have had the Tardis materialize over Mount Doom, dropped the ring into the mountain of fire, and the whole thing is a 45 minute episode rather than a 12 hour trilogy.
5. They both regenerate.
6. They both believe in humans/mortals and put immense power in their hands.
7. The Doctor and Gandalf both have a habit of showing up just when they are most needed, whether you're escaping via the air lock of a space liner or about to be burned to death by a volcano.