What are some motifs in Hamlet?

One motif that recurs throughout is the motif of couples. The suggestion is that just as people come coupled by twos in friendship or love, so do relationships with them come in dualities of two qualities. These dualities can be love and trust or betrayal, which are significant themes of Hamlet. Rosencrantz and Guildenstern are primary examples of this motif and it's impact on the themes.

At the University of Wittenberg, Hamlet held Rosencrantz and Guildenstern in sincere friendship. Once they arrive in Denmark, summoned by Claudius to aid his understanding of the threat Hamlet--the rightful and expected heir to Old Hamlet's throne--does or does not pose him, they quickly and easily turn on Hamlet, betray their friendship and betray him. In contrast, Horatio, whom Hamlet knows as an individual (not as part of a couple), remains true to Hamlet throughout and is the one to execute Hamlet's dying wishes.

Motifs are defined as recurring structures, contrasts, or literary devices that can help to develop and inform the text’s major themes or characterizations. Two motifs in Hamlet deal with incest and misogyny.

Incest and Incestuous Desire: incest runs throughout the play and is frequently alluded to by Hamlet and the Ghost, most obviously in conversations about Gertrude and Claudius, the former brother-in-law and sister-in-law who are now married.

Misogyny: Shattered by his mother’s decision to marry Claudius so soon after her husband’s death, Hamlet becomes cynical about women in general, showing a particular obsession with what he perceives to be a connection between female sexuality and moral corruption. This motif occurs sporadically throughout the play, but it is an important inhibiting factor in Hamlet’s relationship with Ophelia. He urges Ophelia to go to a nunnery rather than experience the corruptions of sexuality.