Fluffy

Fluffy is a vicious, giant, three-headed dog found in the forbidden third floor corridor on the right-hand side.

Fluffy was used as the first line of defense against potentional thieves of the philosopher's stone. As his name suggests, Fluffy belongs to Hagrid, who got him from a Greek person he met in a pub.

The only way to get past Fluffy is to play him music, but Fluffy wakes up the moment the music stops playing. Professor Quirrell got past Fluffy by enchanting a harp to autonomously play music.

In the book Harry Potter and the Philosopher's Stone, Harry, Ron and Hermione used a flute that had been given to Harry by Hagrid.

In the movie by the same name, Professor Quirrell's harp was still playing when Harry, Ron and Hermione arrived. The harp stopped playing unexpectedly while they were still talking so they had to jump into the hole.

Fluffy is based on Cerberus, the three-headed dog from Greek Mythology that guards the gates to the underworld, hence the reason that Hagrid got Fluffy from a Greek person. Like with Fluffy, Cerberus was lulled to sleep by music, though this is more a testment to Orpheus' music skills rather than susceptibility of Cerberus. Note in the film Hagrid said he got Fluffy from an Irish person instead of Greek. This is a mistake. Steve Kloves says when he wrote the script it said "Greek," but was changed somewhere along the line.

J. K. Rowling was asked in an interview what happened to Fluffy after he was no longer needed to protect the Stone. She said Fluffy was released into the Forbidden Forest.

Norbert

Norbert is Hagrid's baby Norwegian Ridgeback dragon.

Hagrid secretly hatched Norbert in his hut from an illegal egg (the Ministry of Magic classifies dragon eggs as Class A Non-Tradeable Goods). Norbert grew at an amazing pace and was very nearly discovered when Draco Malfoy eavesdrops on Hagrid's conversation with Harry and his friends. Harry eventually helps send Norbert to Charlie Weasley in Romania during a midnight escapade up the North Tower in which Harry and his friends are caught and given detentions.