Gideon!
Gideon is the name of not only Gideon Graves (the leader of the League of Evil Exes), but also Ramona's tabby cat. Throughout the series there was a lot of speculation whether the cat was Gideon, but it wasn't, and when questioned about it in the final volume, Ramona said it was "her way of working things out."
Gideon was originally a stray that found its way into Ramona's life, but then became Scott's when she disappeared. Gideon runs off at the end of Book 5, but returns months later to Scott in Book 6 when he's in his new apartment and trying to get life back together. Scott accepts the cat's return since it's the only thing he has that connects him to Ramona while she is gone. The night the cat returns is the first night Scott sleeps soundly since Ramona's abrupt absence(He had been haunted by nightmares of Ramona, Gideon, and other aspects of his girl troubles since her disappearance.)
In vs. the World
SEE? Gideon the cat on Scott's mug!
Gideon had a brief cameo in Scott Pilgrim vs. the World (Movie) on a mug Scott drank out of at the beginning when at Stephen's apartment.
In the Game
It could be possible that the cat seen in World 1 and World 4 (in Ramona's backyard) in Scott Pilgrim vs. the World: The Game could be Gideon the cat.
Gideon in the game.