Preheat oven to 375 degrees F (190 degrees C). Grease cookie sheets.
In a medium bowl, cream together the butter and sugar until smooth. Beat in the vanilla and egg. Combine the flour, baking powder and salt; stir into the creamed mixture. Roll rounded teaspoonfuls of dough into balls, and place 2 inches apart on cookie sheets. Flatten slightly.
Bake for 10 to 12 minutes in the preheated oven. Allow cookies to cool on baking sheet for 5 minutes before transferring to a wire rack to cool completely.
Soft sugar cookies are a classic American treat.
These cookies can be decorated with icing or sprinkles for a festive touch.