Albus Dumbledore

Albus Percival Wulfric Brian Dumbledore is best known as the Headmaster of Hogwarts School of Witchcraft and Wizardry during Harry Potter's six years attending the school.

Character
Dumbledore is widely acknowledged to be very wise and almost omniscient when it comes to goings-on within the grounds of Hogwarts (though he has been known to miss things). He is kind, unfailingly congenial in conversation, and possesses a quirky sense of humor. He is fond of sweets, such as sherbet lemons, Cockroach Clusters, and hot cocoa. All of the above serve to disarm those who underestimate him, leading them to take him for nothing but a potty old man. These invariably find out too late that they've been had. Dumbledore wasn't awarded the Order of Merlin, First Class and made Supreme Mugwump of the International Confederation of Wizards and Chief Warlock of the Wizengamot for nothing. He is, in fact, the most powerful wizard of the age, whatever that young upstart Voldemort might think.

This is probably a good time to mention that Dumbledore is very, very old--111 in Harry's first year at school, according to information collected in the Harry Potter Lexicon. His long hair and beard (long enough to tuck into his belt) are silvery-white, his eyes are light, bright blue, and he is tall and thin. He wears half-moon spectacles and his nose is long and crooked.

Before becoming Headmaster of Hogwarts, Dumbledore taught Transfiguration and was the Head of House Gryffindor. At that time, his hair and beard were a rich auburn.

During Voldemort's first rise to power, Dumbledore founded and led the Order of the Phoenix as a resistance movement, directly opposing Voldemort's Death Eaters. Related trivia: Dumbledore keeps a pet phoenix named Fawkes and his Patronus is, unsurprisingly, a phoenix.

Dumbledore tragically dies at the end of the sixth book, when Severus Snape performs the Killing Curse on him at the top of the Astronomy Tower. In Snape's defense, he was acting at Dumbledore's request and in accord with a previous agreement between them. By killing Dumbledore himself, Snape prevented Draco Malfoy from having to do it and therefore saved him from Voldemort's wrath should the boy have lost his nerve (which he did). It was Dumbledore's wish to not die with his blood on Draco's hands. Also, at that point Dumbledore was already dying of the magical poison he was forced to ingest in order to retrieve one of the Horcruxes, and he was also slowly dying of a curse that he'd incurred as a result of trying to put a Horcruxed-ring on his finger (to explain why would be too much of a spoiler). A quick Avada Kedavra was probably a kinder alternative to slow poisoning. Not that anyone knew any of this at the time.

Relations
Dumbledore is the son of Percival and Kendra Dumbledore. His only living relative at the time of the books is his younger brother Aberforth, who only appears a few times and is known mostly for being rather odd and more than a little dodgy. He was once arrested for performing "inappropriate charms on a goat." A goat also happens to be his Patronus. Aberforth is the publican of the Hog's Head pub in Hogsmeade.

Dumbledore had a sister, Ariana, but she was accidentally killed in the midst of a duel between Albus, Aberforth, and Gellert Grindelwald. Aberforth blamed his brother, but it is unknown who actually fired off the lethal spell. Previous to her death, she was attacked by Muggles and so traumatized that she tried to repress her magic, which led to instability requiring the full-time care of her family. Albus, caught up in his project with Grindelwald, didn't have much attention to spare for his sister, something he regretted until his own death.

Grindelwald was Dumbledore's love interest when they were both teens with great plans to discover the Deathly Hallows and use them to bring order to the Force Wizarding World, but Dumbledore realized how dark Grindelwald's ambitions were becoming and was instrumental in his eventual defeat. It is unknown whether or not Dumbledore had any other serious romantic relationships, but that's probably none of our business anyway.

In Badfic
Dumbledore is often rendered into a cliche, appearing only to award house points, or say a few pseudo-clever lines, or generally look wise and twinkly-eyed. Unfortunately, these attempts often end with Dumbledore looking daft at best, stupid or incompetent at worst.

In Mary-Sue stories wherein the Sue is in Gryffindor, he may overturn punishments handed down by other professors, especially Snape, because the Sue is just that special. Conversely, if the Sue is in Slytherin, Dumbledore may be villainized and shown to unjustly favor students in other houses, especially Gryffindor. He often appears as a relative of a Sue, usually the Sue's father, grandfather, or uncle. In these cases, the favoritism shown the Sue may increase exponentially. Rarely, he may appear as a Sue's love interest despite his age and his known preferences.

Occasionally, he is thrown so far out of character as to be hardly recognizable. The most infamous examples of this are Subjugation and My Immortal. Both of these are Legendary Badfic and neither Work Safe nor Brain Safe.

In crossover fic, Dumbledore is often related to or conflated with Gandalf (in Lord of the Rings) or another old-and-wise archetype character, such as Obi-Wan Kenobi in the original Star Wars trilogy. This rarely goes well.