What are some examples of character foils in Hamlet?

The character foil is a very useful technique for presenting two opposing characters so that they might highlight each other’s differences in temperament, behavior, values, relationships, motives, and so on. Shakespeare employed this literary technique quite adeptly in his dramas, demonstrating how intuitive he was was concerning human nature.
In Hamlet, nearly every character has a foil or two (or three). King Claudius is frequently and openly compared to his predecessor, the brother he murdered. King Hamlet loved his country, his wife, and his son, and he showed that love through protective actions. Even in death, he comes back to warn Hamlet to protect the kingdom and Queen Gertrude from Claudius’s evil behaviors. Claudius, however, has no qualms about killing anyone who gets in his way of having the crown and the queen. Hamlet attempts to show Gertrude the differences between the two men as he holds up a picture of each to her in act 3, scene 4. He says that Claudius is "like a mildewed ear blasting his wholesome brother.” We see the difference clearly, even if Gertrude cannot.
Although most protagonists have a foil, Hamlet actually has several. While the prince’s nature is melancholy and filled with emotional highs and lows, his close friend Horatio is very level-headed and emotionally stable. For example, after Claudius storms guiltily out of the play in act 3, scene 2, Hamlet is erratically happy and energetic, excitedly asking Horatio if he observed Claudius’s guilty response. Horatio calmly replies, “I did very well note him.” We get the sense that Horatio is a little nonplussed by his friend’s inappropriate response. Later, in the graveyard, in act 5, scene 1, Hamlet morosely contemplates the course of Alexander the Great’s body through the earth and into the loam used to stop a beer barrel. Horatio tries to halt the morbid direction of his friend’s thoughts by saying, “Twere to consider too curiously to consider so.” Shakespeare places calm, logical Horatio next to Hamlet to not only act as a leveling presence in the prince’s life, but to highlight Hamlet’s brooding, overly emotional nature.
Another character foil for Hamlet is Laertes. On the surface, they have similar circumstances—a father murdered. Hamlet acknowledges this in act 5, scene 2, when he tells Horatio, “by the image of my cause I see the portraiture of his.” While Hamlet suffers from an inability to act upon his desire for revenge, he contemplates every related thought and opportunity, Laertes is overly rash in his decision-making. Unlike Hamlet, he is willing to damn his own soul to hell for his revenge; he storms the castle in an attempt to kill King Claudius but then succumbs to the king's suggestion to murder Hamlet.
Even Prince Fortinbras of Norway acts as a foil to Hamlet, although though we see little of him in the play. He takes action to expand his future kingdom, bravely commanding an army to fight for land in Poland. Hamlet compares himself to the prince and his army, admiring how they would bravely "go to their graves like beds,” simply because "honor’s at the stake." He admits that he, whose father was murdered and mother ruined, has done nothing, and he uses Fortinbras’s example to spur his own revenge (or at least he contemplates it).
Shakespeare’s Hamlet is rich with other foils, as well, so by the end of the play, he has revealed the psyche of each tragic character.
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