No the Macbeths do not have any children, and this becomes a significant factor in the play. The witches predict that Macbeth will be king, but they then predict that Banquo's children will be king. Because of this, they say that Banquo will not be as great as Macbeth, but much greater. After Macbeth follows through with killing King Duncan, he realizes that he has defiled himself for no reason - Banquo will get all the benefit, because Macbeth's line will end with himself. This realization leads Macbeth to murder and attempt to murder Banquo and his son Fleance. His failure to kill Fleance allows the witches prophecies to come true - Banquo's descendants will take the thrown, and Macbeth's line ends.
It's also interesting to note that Macbeth and Lady Macbeth's inability to have children affects their relationship negatively. Macbeth blames Lady Macbeth for not producing children. It is one of the factors that plays a part in the decline of their relationship throughout the play.