What is Banquo's importance in Shakespeare's Macbeth and how does his role affect other characters?

Banquo in many ways can be seen as a foil to Macbeth. Though Banquo also witnesses the prophecy of the witches, he does not choose to take matters into his own hands. This decision provides us with a marked contrast to Macbeth, who interprets the witches' prophecy as an invitation to murder his way to the throne of Scotland. Interestingly enough, though Banquo makes no effort to act on the prophecy, the witches' prediction still comes true, as it's suggested that Banquo's descendants will become a line of kings. This suggestion makes Macbeth's own actions even more evil, as it implies that individual action (and, by extension, Macbeth's murderous schemes) were not necessary to fulfill the prophecy. 
Banquo affects other characters, especially Macbeth, in significant ways. Appearing at a banquet in a grim and ghostly form, Banquo's spirit inspires dramatic paranoia in Macbeth and causes the king's mental state to unravel. Thus, Banquo's ghost is one of the primary forces that contributes to Macbeth's decline, and so it also sets the stage for the tyrant's downfall.