The character in the Odyssey known for turning men into swine is Circe. She is a powerful sorceress who lives on the island of Aiaia and uses her magical abilities to transform Odysseus' men into animals. However, Odysseus, with the help of the god Hermes, resists her magic and ultimately persuades Circe to revert his men back to their original form. Circe's character illustrates the themes of temptation and transformation in the Odyssey, highlighting both danger and the potential for redemption.