Sift flour, baking powder, and salt into a bowl and set aside.
Using an electric mixer, beat granulated sugar and softened margarine until creamy.
Add eggs one at a time, beating well after each addition, then mix in vanilla extract.
Gradually add sifted dry ingredients to wet mixture and mix until a soft dough forms; avoid overmixing.
Wrap dough in plastic and refrigerate for 2 hours for easier handling.
Preheat oven to 400°F and lightly grease two baking sheets.
Roll dough on a floured surface to 1/4-inch thickness, cut into shapes using cookie cutters, and place on sheets.
Bake cookies 6 to 8 minutes until edges are lightly golden.
Let cookies cool on baking sheets for a few minutes, then transfer to wire racks to cool completely.