In a large mixing bowl, beat together butter and sugar until fluffy. Stir in eggs and vanilla; mix well.
Stir together flour, baking soda and salt, then add to butter mixture, mixing until thoroughly combined.
Divide dough in half and place each half on a piece of plastic wrap. Shape into a log about 2½ inches in diameter and wrap tightly. Refrigerate for at least 2 hours until firm.
To prepare cookies, preheat oven to 400°F Slice dough thinly and place on lightly greased baking sheets. Bake for 8 to 10 minutes or until lightly browned around the edges. Transfer cookies to a baking rack to cool. Store in an airtight container.
Alternatives: Lemon: Sub lemon extract for vanilla and add 2 tsp finely grated lemon zest.
Cherry: Sub cherry extract for vanilla and add 1/2 cup finely chopped dried cherries or dried craisins.
Nut: Add 1/2 cup finely chopped pecans or walnuts.
Chocolate: Stir in 2 squares melted semisweet chocolate.