The Tempest
The tempest (storm) at the beginning of the play is itself a form of irony, as it is a storm conjured by Prospero in an attempt to control the events on the island and win back his dukedom. The audience learns this information rather quickly, but the characters caught in the storm (as well as Miranda) are unaware that Prospero has manipulated nature in order to serve his own ends.
Alonso's Death
In "Ariel's Song," Ariel gives Ferdinand an elaborate description of how his father Alonso's body has been transformed on the ocean floor after he drowned at sea. The song is an example of dramatic irony because Alonso is not actually dead, and he reappears at the end of the play when he is reunited with his son.
Caliban's Language
Early in the play, Caliban tells Miranda that the only benefit he received from learning her language was that he has also learned how to curse her. Later in the play, however, Caliban describes the wonder of the island by delivering what many consider one of the most eloquent speeches in all of Shakespeare's plays. Caliban's relationship to his non-native language is ironic because though he detests Prospero and Miranda for forcing it on him, he has mastered its power and appreciates its complexity.
Ferdinand and Miranda
At the end of the play, Gonzalo comments that Prospero's grandchildren will become kings of Naples (through Miranda and Ferdinand). Gonzalo thus communicates a central irony of the play, which is that it was Prospero's very exile that leads to his increase in power and continued legacy.
