Here is the recipe I have used for the past three years and it never fails me. I found it on Allrecipes and it really is great. It makes a huge batch so cutting all ingredients in half works fine.
The Best Rolled Sugar Cookies
1 1/2 cups butter
2 cups white sugar
1 tsp vanilla extract
5 cups flour
2 tsp baking powder
1 tsp salt
In a large bowl, cream together butter and sugar until smooth. Beat in eggs and vanilla. Stir in the flour, baking powder, and salt. Cover, and chill dough for a least one hour (or overnight).
Preheat oven to 400 degrees F. Roll out dough on floured surface 1/4 to 1/2 inch thick. Cut into shapes with any cookie cutter. Place cookies 1 inch apart on ungreased cookie sheets.
Bake 6-8 minutes in oven. Cool completely.
Sugar Cookie Icing
1 cup confectioners' sugar
2 tsp milk
2 tsp light corn syrup
1/4 tsp almond or vanilla extract
In a small bowl, stir together confectioners' sugar and milk till smooth. Beat in corn syrup and extract until icing is smooth and glossy. If icing is too thick, add more corn syrup.