Gríma son of Gálmód, called the Wormtongue, was a trusted retainer of Théoden, king of Rohan. At some point before the events of the books, he went into the service of Saruman and corrupted Théoden the King, leading him to ignore the threat Saruman posed to his people and sink into a deep depression. For this, Gríma was given the derogatory epithet Wormtongue by Gandalf, who exposed him and released Théoden from his influence.
Gríma is known to have lusted for Théoden's neice, Éowyn. As part of their agreement, Saruman promised that Gríma would have Éowyn if Saruman succeeded in gaining power. He didn't, much to everyone's relief.
In the Movies, Gríma is made extra-creepy by a lack of eyebrows.