Scott's Bass Guitar (well, actually it belongs to Lawrence)
Scott's Bass actually belongs to Scott's younger brother Lawrence West, who loaned it to Scott for an indefinite amount of time. It is a Rickenbacker as the picture above indicates. Scott uses it through out most of the series to play for his band Sex Bob-omb during live performances or band practice. Occasionally, though, he has had to use his bass as a weapon.
In Scott Pilgrim & the Infinite Sadness, Scott beats Todd Ingram over the head with his bass after Todd uses his vegan-powers to attack Envy Adams. This initiates a Bass Battle between Scott and Todd, in which the two bassists use their instruments to create weaponized musical sound waves. Then in Scott Pilgrim vs. the Universe, Scott uses his bass to destroy The Twins' Second Robot at a concert. Unfortunately, the bass breaks in half, leaving Scott without an instrument.
Later, Lawrence comes back along with Scott's Mom & Dad to retrieve his bass. Scott sheepishly returns the bass in its case. Lawrence leaves with his bass, unaware of its condition.
In vs. the World
Scott with his bass in the movie
In the movie, Scott uses his bass to battle Todd Ingram in a Bass Battle. Todd proves to be a better bassist and - combined with his vegan powers - defeats Scott, blowing him away with the power of his bass solo. Fortunately, the Vegan Police show up shortly after and strip Todd of his Vegan powers, allowing Scott to defeat him.
Scott also uses his bass against the Katayanagi Twins during their musical battle. The bass is never mentioned as belonging to Lawrence.
In the Game
Just hit 'em on the head!
In Scott Pilgrim vs. the World: The Game, Scott's bass makes several of appearances, such as the Bass Battle with Todd Ingram (which ends with the player using the bass to hit Todd on the head). The Bass can be wielded by any character during this part of the game. Scott is also seen playing it in the end credits, as well as Stephen Stills' ending.