Preheat oven to 350°.
Combine sugar and water in a small, heavy saucepan. Cook over medium-high heat until sugar dissolves, stirring frequently. Continue cooking 3 minutes or until golden, stirring constantly. Immediately pour into 8 (6-ounce) custard cups coated with cooking spray, tipping quickly until caramelized sugar coats bottom of cups. Cool completely.
Combine rum and remaining ingredients, stirring with a whisk until well blended. Divide the egg mixture evenly among prepared custard cups (about 1/2 cup each).
Place cups in a 13 x 9-inch baking pan; add hot water to pan to a depth of 1 inch. Bake at 350° for 30 minutes or until center barely moves when custard cup is touched. Cool completely in water bath. Remove cups from pan; cover and chill at least 4 hours or overnight.
Loosen edges of custards with a knife or rubber spatula. Place a dessert plate, upside down, on top of each cup, and invert onto plates. Drizzle any of the remaining caramelized syrup over custards.