Cymbeline is often called a "problem play" because it defies traditional categories of genre. Many Shakespeare critics settle on calling it a "tragicomedy" since the first three acts of the play feel like mini-tragedy, while the play's second half feels like a comedy.
In the first three acts, Imogen and Posthumus are separated and torn apart by Cymbeline, the Queen, Cloten, and Iachimo. There's a murder plot (or two or three) and a kidnapping. It seems like the whole thing is doomed by the time Imogen herself "dies," yet, Cymbeline, unlike Shakespeare's full-out tragedies, has a happy ending: families are reconciled, a couple is reunited, and order is restored between the kingdoms.
Plus, only the evil characters (Queen and Cloten) actually die. It's like Shakespeare is punishing the mean characters and giving the good ones happier endings. As anyone who has a read Hamlet or King Lear knows, this is not how things go down in a Shakespearean tragedy. There, good characters are knocked off like flies, and some of the evil characters live to see many more days.
Romance and Fairy Tale
Many critics also refer to Cymbeline as a "romance"—and we're not talking about supermarket novels with steamy couples rolling around in the sand.
Shakespeare's "romance" plays (Cymbeline, The Winter's Tale, Pericles, and The Tempest) were all written at the end of his career and involve the following features: loss and recovery (think of Guiderius, Arviragus, and Imogen all being found and revealed), a wandering journey (think of Posthumus's travels to Rome and back, and Imogen's journey in the woods), and elements of magic and the fantastic (think of Imogen's fake death and Jupiter's random visit to the jail with Posthumus's ghost family).
If you're thinking that all of this sounds a lot like a fairy tale, you're absolutely right—fairy tales, which are notorious for being purposely implausible and fantastical, share a lot in common with "romance" stories. The point isn't realism: these stories are symbolic and archetypal. It's like they're showing us a different kind of reality to help us see new aspects of our everyday reality.