What are some examples of deception and lies in Hamlet?

William Shakespeare's Hamlet explores many rich themes and motifs, but its exploration of deception runs especially deep.
The appearance of King Hamlet's ghost carries with it several noteworthy points regarding deception. The ghost explains to the prince that Claudius—Prince Hamlet's uncle and the late King Hamlet's own brother—was his murderer. The ghost says that Claudius did this deed with the help of the prince's mother, Gertrude. Claudius used the "witchcraft of his wit" to seduce Gertrude, despite her marital vows to the late king.
The ghost despairs, stating that he was a dignified husband and upheld his marriage vows to Gertrude. He asserts that Gertrude lacked the fidelity and honesty that he possessed in their marriage (he refers to her as "a wretch whose natural gifts were poor / To those of mine") and notes that his brother killed him by pouring poison down his ears, which may be a nod to the lies told to him by his wife and brother.

Upon my secure hour thy uncle stole,With juice of cursed hebenon in a vial,And in the porches of my ears did pourThe leperous distilment . . .

In an interesting twist, Prince Hamlet is quite deceptive in this play as well. Famously, Hamlet feigns insanity to justify his odd behavior as he copes with the emotional toll and careful responsibility of avenging his father. Perhaps Hamlet is "fighting fire with fire," so to speak, or perhaps Shakespeare seeks to complicate the classic role of the tragic hero by showing that even heroes who act with caution and virtue aren't above employing deception.