"Fast as a galloping horse" (Simile)
In Act 1, early in the play, Gonzalo, the advisor to the king of Naples, describes the eye of a storm, and uses a simile to express the speed of a storm, which he says is "fast as a galloping horse."
"Like a fountain" (Simile)
In Act 1, Prospero and Ariel discuss trees and the fact that Ariel was imprisoned in a tree when Prospero found him. Ariel talks about the beauty of trees and uses a simile to describe a palm tree, saying, "...springing into the sky like a fountain ending in nonchalant, squid-like elegance."
Uncle Tom (Metaphor)
Several times in their conversations, Caliban calls Ariel an "Uncle Tom," an idiomatic metaphor that originates in Harriet Beecher Stowe's novel Uncle Tom's Cabin and refers to a black slave who is especially obsequious to their white master in hopes of winning favor.
"I am Power" (Metaphor)
After taunting his enemies with the table full of food, Prospero tells Ariel that he wants them to eat it, changing his mind from his original intentions. Ariel questions this change of heart and Prospero insists that changing his mind is his prerogative, and uses a metaphor to describe himself, saying, "I am Power." According to Prospero, not only does he have power, he is power.
"Do it with a gentle tongue, like the toad..." (Simile)
When Caliban awakens from sleep, preparing to resist Prospero, he talks about all the beasts and bugs that have stung him in the night. He then says, curiously, "Or if you really want to lick me, do it with a gentle tongue, like the toad whose pure drool soothes me with sweet dreams of the future."