Fate
In Pericles, fate plays an important role in the rather complicated narrative. Fate often appears in the form of the gods, but it is unclear what stance the gods have on Pericles and his family: on one hand, Pericles seems absolutely riddled with problems and seemingly random trials of his courage and will. On the other hand, it would appear that the gods are protecting Pericles (and other members of his family), despite separating them, ensuring that they will one day be reunited. The play's ambivalent portrayal of fate encourages the audience to question the extent to which free will determines one's future, and to accept that life is often unpredictable and up to forces beyond one's control.
Rebirth
Pericles has puzzled critics for centuries regarding its genre, as it lies somewhere between comedy and tragedy. Most often, Pericles is considered a romance, and scholars often cite the play's focus on rebirth and recovery as a reason for this classification. Like in Shakespeare's other romances, there are many instances in Pericles of what is lost being recovered or what is dead being reborn (Thaisa, for instance). Moreover, the play itself can be considered a story of rebirth, as it was a story from the fourteenth century that Shakespeare "brought back to life" for Renaissance audiences.
Family
Of course, family and family structures play a central role in the action of Pericles. There are loving families (Pericles, Thaisa, and Marina) as well as unhealthy familial relationships, like that between Antiochus and his daughter. The play warns against these dysfunctional familial structures by having Antiochus and his daughter punished by the gods through death by fire. Ultimately, the play is structured so that its main character, Pericles, can start a family, lose that family, and eventually be reunited with his loved ones by the end of the play. This structure helps emphasize the importance of family bonds in association with fate: family members will always be connected, even if they are physically separated.
Power
Pericles is the Prince of Tyre, but he spends the majority of the play in other places: Antioch, Tarsus, Pentapolis, and wandering the seas trying to get home. These travels bring him into contact with a number of different kings and rulers, each of which serves as a foil for the others in terms of how they decide to lead. Antiochus, for example, is an unsavory king who abuses his power (illustrated by his incestuous relationship with his daughter) while Simonides is celebrated for his benevolence and fair attitude toward his own daughter's marriage. Notably, these leaders are all presented to the audience through the same father/daughter dynamic, and how a ruler treats his daughter becomes the metric by which their status as leaders is measured.
Appearance vs. Reality
Pericles undergoes an important transformation over the course of the play, as he learns to read situations with more accuracy rather than judging by appearance alone. In the beginning of the play, for example, Pericles is enthralled by Antiochus's daughter, only to learn that she is having an incestuous relationship with her father. He is later unable to tell that his wife is actually alive, and mistakenly throws her overboard believing her dead. By the end of the play, Pericles has matured enough so that when he encounters his own daughter, Marina, he no longer pays attention to appearances alone but is able to put the pieces together.
Sex
Sex appears in Pericles in pretty stark terms: there are healthy, loving sexual relationships that produce babies and continue the family line (such as that between Pericles and Thaisa). However, there are also perverted sexual relationships (like that between Antiochus and his daughter) as well as immoral sexual indulgences (like those seen at the brothel). These types of sexual encounters are punished in the play: Antiochus and his daughter are struck with fire by the gods, and the patrons of the brothel die from STDs and other illnesses.
Storytelling and the Theater
Pericles is a play that tells an elaborate story, but it is also a play about storytelling itself. The play is narrated by John Gower, the fourteenth-century poet whose work served as Shakespeare's primary source material for the performance. Throughout his narration, Gower reminds the audience that this play is a work of resurrected poetry, brought to life on the early modern English stage. Furthermore, characters provide their own stories to other characters in the play, even when the audience has already seen those stories play out. In structuring Pericles this way, Shakespeare emphasizes the importance of stories in keeping people together while simultaneously touting the theater as the medium through which old stories can be made new again.