Number Twelve, Grimmauld Place
Number twelve, Grimmauld Place has been the house of the Blacks for many years. Sirius donated it to the Order so that it could be used as headquarters; in that capacity, the house was protected by the Fidelius Charm, with Albus Dumbledore as its Secret Keeper (OP4). After Sirius' death, Harry, his heir, was determined that the house continue to be used by the Order (HBP3).
Sirius was confined to the house for much of Harry's fifth-year at Hogwarts, much to his dissatisfaction. Arthur, Molly and the Weasley children were infrequent companions, as were Harry himself and Hermione; for the most part, Sirius gloomily remained in number twelve on Dumbledore's orders along with Buckbeak. Harry once noticed a smell that might have indicated that his godfather had been drinking his pains away (OP22).
Kreacher, the Blacks' house-elf, is figuratively tied to the house. His ownership and duties vary according to the identity of the proprietor of number twelve. Because of that, after Sirius' death, Harry Potter becomes the elf's master, much to the creature's disgust, who would have preferred to work for Bellatrix or Draco. Kreacher remains loyal to the Blacks' ideals of blood status, and is constantly found muttering and complaining about the undignified visitors to the house, notably Remus Lupin, Hermione Granger and the Weasleys.
When Sirius started purging the house of all elements pertaining to old Black history, Kreacher desperately tried to salvage as much as he could. The house-elf is especially obsessed with Walburga Black, mother of Sirius and Regulus; he constantly wails that she would have been extremely disappointed to see what the house has become.
Other than Sirius, Buckbeak, and Kreacher, the only inhabitants of number twelve, Grimmauld Place are its paintings, notably that of Phineas Nigellus Black—which allows him to bring messages back and forth between the house (more specifically, the room where Harry usually sleeps when there) and the Hogwarts Headmaster's office—and of Walburga Black, which tends to scream, holler and wail whenever a somewhat loud noise is made. Sirius tried to remove his mother's painting, but she stuck it to the wall, and so he could not move it.
Peculiar parts of the house
The Blacks are, for the most part, notably obsessed with blood purity, and have several old family traditions, such as that of chopping off the heads of house-elves that became too old to carry trays. Since the time of Elladora Black, who first came up with that particular habit, the heads have been on display in a corridor (OP6).