Preheat the oven to 350 degrees. Grease and flour three, 8-inch round cake layer pans or, two, 9-inch round cake layer pans. Sift the flour with the baking powder and salt; set aside. In a large bowl, beat the butter, sugar, eggs and vanilla at high speed until light and fluffy-about 5 minutes. Occasionally scrape the sides of the bowl while beating. Beat in the flour mixture at low speed in fourths, alternately with the milk, in thirds. Begin and end with the flour mixture. Beat only until smooth. Pour the batter into the prepared pans and bake for 30 to 35 minutes, or until a cake tester comes out clean or the middle springs back when lightly touched with a fingertip. Cool in the pans for 10 minutes and then turn out onto wire racks to cool completely. Fill and frost as desired.