Arrange 24 wooden sticks on well-buttered baking pans, and set aside.
Combine sugar, water, vinegar, and butter in a 2-quart saucepan. Cook over medium heat, stirring constantly, until sugar dissolves. Cover and continue to cook over medium heat 2 to 3 minutes to wash down sugar crystals from sides of pan. Uncover and cook, without stirring, until mixture reaches hard ball stage (260°). Remove from heat, and stir in vanilla.
Immediately drop mixture by tablespoonfuls onto alternate ends of each wooden stick. Allow suckers to cool completely before removing from pans. Wrap each sucker tightly in plastic wrap.