How is Macbeth and Banquo's relationship affected by the prophecies of the witches?

Macbeth and Banquo have a good, positive relationship at the opening of the play. As generals in King Duncan's Scottish army, they fight together to defeat the Norwegians and rebellious Scots. Shortly after their victory, however, they encounter the witches, who make several prophecies. One is that Macbeth will become Thane of Cawdor and king. When Banquo asks what the future holds for him, the witches say that he shall “. . . get 'kings,” which means that his descendants shall become kings.

At first, Banquo and Macbeth do not directly address the implied conflict here—if Macbeth is going to be king, but Banquo's descendants are going to become kings, something negative is going to have to happen to Macbeth's royal line.

Later in the play, after Macbeth has achieved the throne, Banquo, speaking alone on stage, expresses his suspicions of Macbeth's path to the kingship:

Thou hast it now; king, Cawdor, Glamis, all,

As the weird women promised, and I fear

Thou play'dst most foully for't:

Soon thereafter, Macbeth is alone on stage and relates this worry concerning Banquo:

To be thus is nothing;

But to be safely thus; our fears in Banquo

Stick deep; and in his royalty of nature

Reigns that which would be fear'd.

Macbeth means that even though he has become king, it doesn't mean anything unless he is safe, which he is not as long as Banquo is alive.

In the next scene Macbeth arranges for Banquo and his son Fleance to be murdered.

Thus, the witches' prophecies have shattered the relationship between Macbeth and Banquo by causing them to become suspicious and afraid of each other.