In a 2 quart saucepan, combine sugar, cornstarch, and salt. Slowly stir in milk. Bring to a boil, and cook, stirring constantly, over medium heat until mixture thickens. Cook for 2 to 3 minutes more. Stir in vanilla.
Pour hot pudding into dessert glasses or molds that have been rinsed in cold water. Chill until firm. Unmold if desired. Serve.