Beat butter at medium speed with an electric mixer until creamy; gradually add sugar, beating well. Add eggs and vanilla extract; beat until blended.
Combine flour, baking powder, and salt. Add to butter mixture, beating at low speed until blended. Shape dough into 2-inch balls, and place 1 inch apart on ungreased baking sheets. Flatten balls slightly with bottom of a glass dipped in sugar.
Bake at 325° for 10 to 12 minutes or until golden (do not brown). Transfer to wire racks to cool.