Certainly, Iago, from Othello, must top the list of Shakepeare's villains. He is a treacherous, malicious, underhanded liar who cares about nobody but himself and will stop at nothing to destroy Othello's happiness by turning him against the innocent Desdemona.
Claudius, Hamlet's uncle and stepfather, never repents of cold-bloodedly murdering his brother to gain the throne of Denmark—and is as willing to murder his brother's son, Hamlet, to keep himself securely on the throne.
King Lear yields up three especially notorious villains: Lear's two eldest daughters, Goneril and Regan, and Gloucester's illegitimate son, Edmund. The sisters are especially cruel in the treacherous way they turn on their father as soon as they have his power. Edmund, like Iago, using devious plots and plans to estrange his father from Edgar. This loathsome trio use each other, with Edgar sleeping with both daughters and playing them off against one another. Other acts include throwing their elderly father out of the house into a storm and blinding Gloucester.
Richard III, from the play of that title, is another treacherous figure who arranges for the murder of his young nephews in the Tower of London: he is a creepy, wily figure who will do anything to keep the throne.
Macbeth starts out as a normal person and heroic fighter, but as he murders his way to power becomes a classic Shakespeare villain. He loses all compassion and joy and stoops, by the end of the play, to murdering innocent children. Lady Macbeth is often listed as a top villain, too, because of the ruthless way she goads her husband into murdering Duncan. I would say she does not quite fit the paradigm, because she does feel such intense guilt over what she has done that she commits suicide, but she is usually put on the top villain lists.
While Measure for Measure is a dark comedy, Angelo, left in charge of Vienna, acts in the mode of the classic villain, showing himself to be a coldhearted hypocrite who behaves deceitfully and preys on the innocent. In a similar vein, though he appears in a comedy, The Tempest's Antonio fulfills the villainous role, betraying his brother, stealing his throne, and setting Prospero and his young daughter out in a leaky boat to die at sea.
All of these individuals (which the exception of Lady Macbeth) are heartless, treacherous, unrepentant murders—or would-be murderers—who victimize the innocent to achieve their own ends.