Beat together butter, powdered sugar and vanilla until well blended. Add flour, one cup at a time, to butter mixture.
On a floured surface, roll out dough to 1/4 to 1/2-inch thickness. With a sharp knife, cut dough into 2-inch squares or cut into 1 3/4-inch rounds with a cookie cutter.
Place on an ungreased baking sheet and prick top of cookies with a fork. Bake at 325° for 20 minutes, or until bottoms are golden and tops are light in color. Cool on wire racks. Store in an airtight container.