Before the Battle of Hogwarts started he was pushed through a window into the castle with Hagrid, then ran off when a nearby vase was blasted off its plinth. It is presently unknown if he survived.
A giant three-headed dog. Purchased from a "Greek chappie" in a pub, Hagrid lent Fluffy to Professor Dumbledore in 1991 to help protect the Philosopher's Stone. Hagrid reveals that Fluffy can be calmed and put to sleep by music, a reference to the mythical Greek story of Orpheus, a minstrel who married a nymph named Eurydice. When she died, Orpheus journeyed to the underworld, where he lulled the hell-hound Cerberus to sleep with his beautiful music in his quest to be reunited with his wife. It is this slip of the lip that allows Professor Quirrell, Harry, Hermione and Ron to all get past Fluffy and into the hall where the Philosopher's Stone is hidden. 
A Norwegian Ridgeback dragon. Hagrid won Norbert's egg from a hooded man (Professor Quirrell/Lord Voldemort) at the Hog's Head during a card game. As dragon breeding was outlawed by the Warlocks' Convention of 1709, Hagrid could not legally keep Norbert. Draco Malfoy spotted Norbert, and tattled on Hagrid, who was forced to send him to Romania.
Norwegian Ridgebacks breathe fire. Nesting mothers breathe on them to keep them warm, explaining why Hagrid kept the egg in a pot over the fireplace in his home, even in warm weather. A pet dragon such as this one, once it hatches, should be fed brandy mixed with chicken's blood.
An enormous talking Acromantula with a taste for human flesh. Aragog's egg came into Hagrid's possession when Hagrid was a student at Hogwarts, he bought it from a traveller. The spider hatched and was hidden at the school in a cupboard; he never saw any other part of the castle.  Hagrid was eventually forced to set Aragog free when his presence in the school became worrisome and Aragog was framed for causing Moaning Myrtle's death. Even then, Hagrid was expelled, and Aragog made a den deep in the Forbidden Forest. He lived there with a large community of Acromantulas until his death.
Aragog met Harry and Ron in 1992, when Hagrid was briefly taken into custody at Azkaban for allegedly opening the Chamber of Secrets. It was through Aragog's explanation of events that Harry and Ron learned Hagrid was innocent of those charges.
Aragog died in the spring of 1997 of old age. The Acromantulas living in Aragog's den tried to prevent Hagrid from removing the body from the Forbidden Forest; Hagrid managed to escape, intent upon giving the Acromantula a proper burial. Professor Horace Slughorn attended the funeral for the sole purpose of procuring some of Aragog's venom, which he felt he could sell for a hundred Galleons a pint. It was because of these events leading up to Aragog's funeral that Harry, under the influence of Felix Felicis, managed to secure Slughorn's memory regarding Voldemort and Horcruxes.
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It is during this class that Buckbeak injures Draco Malfoy. Through the influence of Lucius Malfoy, Buckbeak is sentenced to death by the Ministry of Magic, to be carried out in the coming Spring. However, he is rescued by Harry and Hermione, through the use of the Time-Turner.
Buckbeak then joined Sirius Black, aiding his escape from custody at Hogwarts. The two of them relocated to an unknown country.
Buckbeak appeared again at 12 Grimmauld Place in the spring of 1995. At some point, Buckbeak was injured by Sirius' house-elf Kreacher; when Harry attempted to contact Sirius through the Floo Network, Sirius was tending to Buckbeak's injuries.
After Sirius' death, Harry inherited Buckbeak's companionship, along with Sirius' material possessions. Harry, in turn, returned Buckbeak (rechristened "Witherwings" to protect his identity; Buckbeak was supposed to be a fugitive of the law) to Hagrid's care. During the First Battle of Hogwarts, Buckbeak saved Harry from the harm of Snape.
Behind the scenes
- This notion of a three-headed dog guarding the doorway to unknown doom is most likely a reference to Cerberus, the hellhound that guards the entrance to the Underworld in Greek mythology.
- Harry Potter and the Philosopher's Stone (First appearance)
- Harry Potter and the Philosopher's Stone (film)
- Harry Potter and the Philosopher's Stone (video game)
- Harry Potter and the Chamber of Secrets
- Harry Potter and the Chamber of Secrets (film)
- Harry Potter and the Chamber of Secrets (video game)
- Harry Potter and the Prisoner of Azkaban
- Harry Potter and the Prisoner of Azkaban (film)
- Harry Potter and the Prisoner of Azkaban (video game)
- Harry Potter and the Goblet of Fire
- Harry Potter and the Goblet of Fire (film)
- Harry Potter and the Goblet of Fire (video game)
- Harry Potter and the Order of the Phoenix
- Harry Potter and the Order of the Phoenix (film)
- Harry Potter and the Order of the Phoenix (video game)
- Harry Potter and the Half-Blood Prince
- Harry Potter and the Half-Blood Prince (film)
- Harry Potter and the Half-Blood Prince (video game)
- Harry Potter and the Deathly Hallows (Possible appearance)
- Harry Potter and the Deathly Hallows: Part 2 (Possible appearance)
- Harry Potter and the Deathly Hallows: Part 2 (video game) (Possible appearance)
- LEGO Harry Potter: Years 1-4