Scabbers was Ron Weasley’s pet rat, until he wasn’t anymore. Scabbers was actually Peter Pettigrew in his Animagus form. After tricking Sirius, Pettigrew transformed into a rat and stayed that way for twelve years, from November 1981 to June 1994, living as Percy and then Ron’s pet, Scabbers, in order to hide from the Death Eaters who thought he had betrayed Voldemort.
As Scabbers, Pettigrew was not fond of Hermione’s cat, Crookshanks, and with good reason. Crookshanks is part Kneazle, which means that he can sense duplicity. He saw right through Peter’s disguise and tried to attack him whenever he got a chance.
The witch behind the counter at the Magical Menagerie in Diagon Alley remarked at Scabbers' long life, but didn't detect that he was actually a wizard in Animagus form:
"Bang him on the counter," said the witch, pulling a pair of heavy black spectacles out of her pocket.
Ron lifted Scabbers out of his inside pocket and placed him next to the cage of his fellow rats, who stopped their skipping tricks and scuffled to the wire for a better took.
Like nearly everything Ron owned, Scabbers the rat was secondhand (he had once belonged to Ron's brother Percy) and a bit battered. Next to the glossy rats in the cage, he looked especially woebegone.
"Hm," said the witch, picking up Scabbers. "How old is this rat?"
"Dunno," said Ron. "Quite old. He used to belong to my brother."
"What powers does he have?" said the witch, examining Scabbers closely.
"Er --" The truth was that Scabbers had never shown the faintest trace of interesting powers. The witch's eyes moved from Scabbers's tattered left ear to his front paw, which had a toe missing, and tutted loudly.
"He's been through the mill, this one," she said.
"He was like that when Percy gave him to me," said Ron defensively.
"An ordinary common or garden rat like this can't be expected to live longer than three years or so," said the witch. "Now, if you were looking for something a bit more hard-wearing, you might like one of these --"
She indicated the black rats, who promptly started skipping again. Ron muttered, "Show-offs." (PA3)
'scabby' means either covered in scabs or loathsome and despicable. Seems an odd name to give a pet.
Just how and when Scabbers managed to ingratiate himself into the Weasley household is unclear. If Percy had him for a pet for a few years, we might guess that Pettigrew "joined" the family in the mid- to late-1980s. Where he was in the years between is never stated. One can't help but wonder if Pettigrew sneaked off into the paddock near the Burrow now and then to transform back into his human form, just to stretch his legs as it were. And if so, why Ginny never cottoned on. That girl doesn't miss much.