First, remember a motif is an idea, symbol, or character the occurs over and over throughout a piece that has significant value (or meaning) to the text.
There are several motifs in Hamlet. Incest is seen from the beginning as we see that Hamlet's mother has married her deceased husband's brother. He constantly refers to his mother as her husband's sister-in-law and Claudius as her brother-in-law.
As Hamlet becomes more and more enraged at his mother's marriage, misogyny (a hatred of women) develops through the play. He yells at Ophelia to go to a nunnery and questions her honesty. These questions and attacks stem from his distrust of women.
Spying can be seen throughout the play. As Polonius attempts to find the cause of Hamlet's depression, he spies on his interactions with Ophelia. He also sends Reynaldo to Paris to spy on his own son, Laertes. Spying ends up being his downfall as he arranges to spy on Hamlet's discussion with Gertrude and is stabbed through a tapestry.