Not much is known about the banjo so far, but Wander is known to use it a lot whenever he sings.
Its next usage is in "The Good Deed", the first time it's used more than once. It's first used when Wander and Sylvia were strolling at the start. Second, Wander used it to play "the appropriate racing-the-clock action music" when getting Fleeblebort to his wedding. Lastly, he played it while passing Lord Hater after his ship explodes and also refusing to help him.
In "The Box", Sylvia gives Wander the banjo to get his mind off thinking what's in the box that has to be delivered, to which he proclaims he always cheers up when he sings. He ends up singing about what's in the box however, leading Sylvia to crush it (though it's fixed in later appearances). This episode is also the first time Wander is seen tuning it. Strangely though, as seen in "The Good Deed", it does not have any tuning pegs.
The fourth usage is in "The Little Guy", where it seems to be seen onscreen longer than any other appearances. It's first used when Wander and Sylvia were relaxing before the weather changes, which eventually leads to them being chased by the Watchdogs. Wander plays his banjo throughout the entire chase scene. Later when Sylvia saves Westley, Wander is briefly seen sitting by a tree playing his banjo, just before standing up and acting a Watchdog has caught him. Later on, Wander takes out his banjo and uses it to play soft music during a soup dinner, he plays it throughout the majority of that scene. Then during the security camera footage, Wander is shown playing the banjo in the jail cell. Finally, Wander has his banjo out while Westley comes back reformed, and he uses it to play the song Wander Over Yonder End Title Theme.
In "The Brainstorm" Hater rejects Peeper's "Mind Combobulator" plan because according to Hater "Wander's banjo will just happen to match the combobulator's frequency causing it to explode, etc." Also, After Peeper explains his entire plan, Hater says "Banjo" without a great reason why. (Ironically, by the end Wander had defeated Lord Hater, Commander Peepers, and all of the watchdogs, with ease with his banjo, destroying Lord Hater's ship.)
The banjo's pot is rounded, with an off-white head in front and back. The pot is black, and has chesnut petals and white circles going around the head, and a black circle with a gold star on the back. The sides of the pot are light chesnut. The neck is light taupe, and a few sections have circular frets. The peghead is black and has two gold stars on it.