Much of Hamlet deals with plotting and scheming. Who in the play sets plans in motion?To what ends?

Claudius is involved in much of the plotting. In fact, one might say that he sets everything in motion through the murder of King Hamlet. When we first see him, he sends messengers to old Fortinbras to plan against young Fortinbras behind his back. He spies on Hamlet through Rosencrantz and Guildenstern, calling them to Denmark solely for that reason. He uses Ophelia for this end as well, plotting with Polonius to use her as bait. He also schemes to send Hamlet to England, and we later find out that he actually arranged for Hamlet's execution. Finally, he plots with Laertes to kill Hamlet in the duel.

Polonius is the next schemer of the play. Although he appears foolish, often long-winded and making little sense, he sees through Hamlet's feigned madness and suspects something underneath. He sens Reynaldo to Paris to spy on Laertes, even instructing him to tell lies & spread rumors about his son. He freely sets his daughter out as bait to "catch" Hamlet faking his insanity. He also hides in Gertrude's closet to eavesdrop on her conversation with her son.

Hamlet too is deeply involved in schemes. He first decides to fake his madness, in order to extract information from various sources. He writes a play & arranges for the actors to perform it, so that Claudius might reveal his guilt. Whether he does so is open to interpretation, but Hamlet is certainly convinced. He also steals his own execution letter on the way to England, & exchanges it for one with Rosencrantz and Guildenstern's death orders.

A few other characters are involved in schemes in the play as well. Laertes plots with Claudius to kill Hamlet, although he feels justified, since Hamlet killed his father. He plans the poison-tipped sword for their duel, & confesses when the plan goes awry. Rosencrantz and Guildenstern, however unintentional their actions may seem, exist in the play only to serve as surveillance on Hamlet for Claudius.

To what ends these schemes and plots? Claudius' death, Gertrude's death, Ophelia's death, Hamlet's death...see a pattern?