Heat oven to 350 degrees F. Grease two 9 x 2-inch-round cake pans, or two 9 x 9 x 2-inch-square cake pans, or one 13 x 9 x 2-inch cake pan. Line with waxed paper; grease paper.
Stir together flour, baking powder and salt in medium-size bowl.
Beat together butter and sugar in large bowl until pale and fluffy, about 5 minutes, scraping down side of bowl with rubber spatula as needed. Beat in eggs, one at a time, until blended. Beat in vanilla. Alternately stir in flour mixture and milk, beginning and ending with flour, just until mixed. Pour batter into prepared pans, dividing equally.
9-inch-round cakes 25 to 30 minutes; 9-inch-square cakes 35 to 40 minutes; 13 x 9 x 2-inch cake 45 to 50 minutes; or until wooden pick tests clean. Cool cakes in pans on rack 5 minutes. Remove cakes to rack to cool. Makes 12 servings (two 9-inch-round cakes, or two 9-inch-square cakes, or one 13 x 9 x 2-inch cake).