In a large bowl, cream together butter and sugar until smooth. Beat in eggs and vanilla. Stir in the flour, baking powder, and salt.

Divide the dough into two portions. Place each piece between two pieces of wax or parchment paper — there's no need to dust the dough with flour. Roll the dough out between the sheets of wax paper to about a 1/4 inch thick. Chill the dough for about an hour in the fridge.

Near the end of the chilling time, preheat oven to 400 degrees F (200 degrees C). Peel off the wax paper from the chilled dough, and on a clean very lightly floured surface cut out shapes with cookie cutters. Place cookies 1 inch apart on ungreased cookie sheets.

Bake 6 to 8 minutes in preheated oven. Cool completely.