Preheat oven to 375°F. In a large bowl, cream butter and sugar with an electric mixer. Beat in eggs and vanilla. Add baking powder and flour one cup at a time, mixing after each addition. Dough will be stiff. Do not chill dough. Divide dough in half. Roll each half about 1/8 inch thick. Dip cutters into flour before each use. Bake cookies on ungreased cookie sheet on middle rack of oven for 8-12 minutes, or until cookies are lightly browned.