While there are many characters in The Tempest, I would consider four to be the "main characters."
Prospero is the play's protagonist. Formerly the duke of Milan, he is overthrown by his brother, Antonio. He flees by boat to an island and spends twelve years harnessing and perfecting his magic. He now seeks revenge.
Ariel is a sprite in service to Prospero. Prospero finds Ariel trapped in a tree and frees him. In return, Ariel agrees to serve Prospero for a year. Prospero has been on the island for twelve years, so the reader does not know if Prospero saved Ariel a year prior or if Prospero simply refused to set him free after the agreed upon period. Ariel possesses an extraordinary amount of magic, making him crucial in Prospero's plans.
Miranda is Prospero's daughter. Having known very little of life outside of the island, she is compassionate and non-judgmental but also shy and passive.
Caliban is the son of Sycorax, the witch who originally imprisoned Ariel. Being the only true native of the island, Caliban feels that Prospero has stolen his home away from him. He maintains that he and Prospero suffer from the same dilemma in regard to being usurped.