In Act 1, Scene 2, Caliban claims to Prospero and Miranda that when they first came to the island, "I loved thee and showed thee all the qualities o' th' isle." But Prospero quickly sets the record straight, asserting that he treated Caliban with "humane care, and lodged thee in mine own cell, till thou didst seek to violate the honor of my child." Then Caliban laughs and agrees, saying, "Would 't had been done! Thou didst prevent me. I had peopled else this isle with Calibans." So Caliban attempted to violate her, but was prevented from carrying out his will.

Miranda, for her part, says that Caliban is a villain whom she does not love to look upon. Miranda had invested in his education, personally teaching him to speak their language. She calls him an "abhorred slave," pointing out that no goodness can be imprinted on his character but that he is "capable of all ill." Caliban hasn't quite given up on his plans for Miranda. Later, in Act 3, Scene 2, he describes her as the main reason Stephano and Trinculo should overthrow Prospero--that "she will become thy bed and bring thee forth a brave brood."

Caliban's interest in Miranda makes him all the more disgusting and makes the poor treatment he receives at Prospero's hands understandable.  

Yes. Caliban did try to rape Miranda and boasts of his deed. Prospero confronts him in 2.1.350-51. He says that while he was his guest, Caliban attempted the rape. He rails: "In mine own cell/till thou didst seek to violate/The honor of my child."

Not abashed at all, Caliban replies that he wishes he had succeeded in the rape of Miranda: "O ho, O ho! Would'st had been done!/Thou didst prevent me; I had peopled else/This isle of Calibans." This last bit means that not only would he have done it once, but repeatedly, until the isle was full of his offspring. Quite a slap...