Furrball's mentor and favorite teacher at school is Sylvester the Cat, although the two similarities only seemed to include their appetites.
Furrball is usually depicted as living in a cardboard box in a back alley or as an unwilling pet of Elmyra, (in spite of the latter, he was absent from the spin-off Pinky, Elmyra and the Brain). In contrast to most of the other characters, he did not speak and was portrayed as a typical pet character (such as in the Porky Pig and Sylvester cartoons, in which Sylvester appears in to have a rare non-speaking role).
Furrball spent much of his time trying unsuccessfully to eat Sweetie Pie, a pink canary; and Li'l Sneezer, a baby mouse with many allergies and hurricane-force sneezes. However, there has been one occassion where Furball got the last laugh on Sweetie when he had Arnold the Bulldog to be hypnotized to chase her after recovering from the hypnosis she put him under.
As the intro suggests, Furrball is prone to misfortune ("unlucky" in the intro) and dealing with his main enemy, Spiky the bulldog. Furrball has also proven to be one of the most versatile characters on the entire show. Some of his many misadventures included getting a pair of malfunctioning 3-D glasses glued to his head, being hypnotized into trying to eat Arnold the Pit Bull for supper, becoming the host of a family of singing Italian fleas, being the terrified love-interest of an amorous Fifi Le Fume after involuntarily winding up with a white stripe down his back, and being chased by the temporarily transformed Sweetie, a large, carnivorous, evil-eyed, feathered Mr. Hyde-Frankenstein monster who wants to eat Furrball.
Furrball also had a bad encounter with Byron Basset, who prevented Furrball from trying to eat some baby birds that he was protecting. Usually, though, the two of them are seen as living peacefully together, not paying much attention to each other and minding their own business.
Although several appearances compared him to Sylvester, there were a few cartoons that cast him in a more sympathetic light. In these appearances, Furball is an abandoned alley cat, constantly looking for a home. The shorts would depict his misadventures in this goal, such as being mistaken for a dog by a blind couple; situations that were humorous, but also gathered pity for the character. He was a lonely cat against the world, but never gave up hope, much like legendary comedian Charlie Chaplin.
As Furrball hardly ever spoke throughout the show, his typical cat sounds are provided by Frank Welker. However, it is revealed that he speaks in three episodes. In the episode Duck Trek (in which Furrball played a spoof of Star Trek's Leonard McCoy), he was voiced by Rob Paulsen (actually, he was lip-synching). In the episode Buster and the Wolverine (a spoof of the classic musical children's story, Peter and the Wolf), it is revealed that Furrball is voiced by his regular voice actor, Frank Welker. In the episode Hare Today, Gone Tomorrow, he speaks precisely one word ("Years!", referring to how long he had been held captive by Elmyra; of course, he was exaggerating), with his voice again being provided by Welker. At the end of one episode after he and Dizzy Devil exposed the Perfecto Prep students' cheating at a baseball game, they both said at a victory party this one line: "We love Baseball". Through the majority of the show, Furrball was in fact a mute.
Furrball's end tag credit is him roaring at the screen like a lion, before covering his mouth and letting out an apologetic mew.