Is Macbeth a static or dynamic character?

Macbeth is a dynamic character because he does fundamentally change over the course of the play.  Initially, he is described as "brave" (1.2.18) and "valiant" (1.2.26), and he is awarded a new title as a result of his courageous and loyal service to the crown: he becomes the new Thane of Cawdor when the old one is executed for disloyalty.  Even his wife, the person who (potentially) knows him the best, thinks that he is "too full o' th' milk of human kindness" to ever do anything to betray his king—a man who is also his kinsman and friend (1.5.17).
By the end of the play, however, Macbeth has not only murdered Duncan (a crime for which he, admittedly, does feel a great deal of guilt), he also arranged for the murders of his best friend, Banquo, as well as Banquo's young son, Fleance.  (Fleance, unfortunately for Macbeth, succeeds in escaping with his life.)  In fact, at this point in the play he tells his wife, "We are yet but young in deed," meaning that they will have to continue killing in order to secure their positions as king and queen (3.4.176).  Additionally, Macbeth arranges to have the innocent wife and children of a rival, Macduff, killed in their home; he does so with no evidence of guilt or remorse.  By the end of the play, he has become a callous killer, much changed from the Macbeth we met in the beginning.