Preheat oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a medium bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Combine the flour and baking powder; stir into the creamed mixture.
Roll dough into walnut sized balls and place 2 inches apart on prepared cookie sheets. Flatten each ball with a fork dipped in sugar.
Bake for 8 to 10 minutes in preheated oven. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.