Dumbledore was related to his immediate family: His father, who was sentenced to life in Azkaban for killing the three Muggles who attacked Dumbledore's younger sister Ariana. Aberforth Dumbledore is Albus's brother, and he runs the Hog's Head inn in Hogsmeade. Dumbledore's mother, Kendra, was accidentally killed by Ariana, during one of her out-of-control fits. The family was not originally from Godric's Hollow, so I don't think there's a significance to Dumbledore, Godric's Hollow, and Godric Gryffindor. Because Dumbledore has red hair and blue eyes, there have been a thousand theories that Dumbledore is a Weasley, particularly Ron. JKR has debunked all these rumours. There is nothing in canon that identifies further individuals as being related to Dumbledore except the following.
Dumbledore also has a "maiden aunt" Honoria, who called off her engagement to a wizard in the Improper Use of Magic Office because she discovered "he had a hairy heart". It was rumoured, however, that she actually discovered him in the act of fondling some Horklumps, which she found deeply shocking (Tales of Beetle the Bard - page 106 - Collector's Edition).