In "Macbeth," what is the significance of the form each apparition takes?
Concerning your question about Shakespeare's Macbeth, the forms of the apparitions in Act 4.1 are significant and connect to other elements of the play. The enotes Study Guide on the play summarizes their part of the scene like this:
The first Apparition is that of an armed head saying he should beware of Macduff. The second Apparition is that of a bloody child and it states that no man born of woman will harm Macbeth. The third Apparition is that of a crowned child holding a tree. This Apparition says, “Macbeth shall never vanquished be until Great Birnam Wood to high Dunsinane Hill shall come against him.”
The helmeted head suggests a warrior, of course, but it also may be reminescent of what Macbeth does to the traitor Macdonwald in Act 1.2.22-23:
...he unseamed him from the nave to th' chops,
And fixed his head upon our battlements.
Macbeth put the traitor's head on a spear and displayed it. Of course, eventually, Macbeth will lose his head, as well.
The bloody child contributes to the blood imagery ever present throughout the play (bloody Captain who tells Duncan about Macdonwald's fate; bloody hands; baboon's blood for the cauldron, etc.). And also adds another child to the mix of children mixed with bloody situations: Fleance, who is targeted for death and witnesses his father being killed, and Macduff's son, who is killed.
The crowned child holding a tree echoes the statement it makes regarding Birnam Wood. Any crowned child is also a threat to Macbeth, since Banquo's heirs have been predicted to be kings, and Fleance escapes his assassins.
There well may be more significance to the forms of the Apparitions than I reveal here. I haven't really thought about this topic much. My ideas should give you a basic set of ideas concerning the forms of the Apparitions, though.