In a medium saucepan combine the water and sugar. Cook and stir over medium heat until sugar is dissolved. Remove from heat; cool about 30 minutes. Stir in the espresso and, if desired, anisette liqueur. Pour into a 13x9x2-inch pan.
Cover and freeze about 1-1/2 hours or until mixture is slushy on the edges. Stir, scraping the frozen mixture off bottom and sides of pan. Cover and freeze for 3 to 3-1/2 hours or until all of the mixture is slushy, stirring every 30 minutes. Cover and freeze for at least 6 hours or until firm.
Before serving, let stand at room temperature for 5 to 10 minutes. Scrape the surface of the granita and spoon into chilled dessert dishes. Makes 8 servings.