Preheat oven to 375°. In a large bowl, cream butter and sugar until light and fluffy, about 5 minutes. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Combine the flour, baking powder and salt; gradually add to the creamed mixture (the dough will be soft). , Drop by tablespoonfuls 2 in. apart onto greased baking sheets. Bake until the edges are golden brown, 7-8 minutes. Remove to wire racks to cool.