In a large bowl, cream butter and sugar until smooth. Beat in eggs and vanilla. Stir in flour, baking powder, and salt. If dough is dry add 1 tablespoon of water at a time and blend well until you get a dough that holds together well, but is not wet or sticky.
Chill dough at least one hour or overnight.
Preheat oven to 400°F.
Roll out dough on floured surface, ¼- to ½-inch thick. Cut into shapes or rounds. Place cookies 1 inch apart on ungreased parchment-lined baking sheets.
Bake 6-8 minutes. Cool on pan for 5 minutes, then transfer to cooling racks.