A good recipe for moist carrot cake is from My Recipes and features cream cheese frosting. Some other good recipes include Grandma Hiers' carrot cake from the Food Network and Best Carrot Cake from Taste of Home.
Make super moist carrot cake with cream cheese frosting by combining 1 box of yellow cake mix, 1 package of vanilla instant pudding and pie filling, 2/3 cup of orange juice, 1/2 cup of mayonnaise and 4 eggs. Stir in 2 teaspoons of ground cinnamon, and fold in 3 cups of grated carrots, 1/2 cup of golden raisins and 1/2 cup of chopped pecans. Pour into a cake pan, and bake at 350 degrees for 35 to 40 minutes.
Whip together 1 8-ounce package of softened cream cheese, 1/2 cup of softened butter, 3 cups of confectioners' sugar, 2 tablespoons of orange juice and 1 tablespoon of grated orange peel. Frost the cake once it cools.
Another good recipe uses 1 can of drained unsweetened pineapple along with the carrots, raisins and walnuts, and it replaces the mayonnaise with vegetable oil. Instead of using instant vanilla pudding mix, you can use 1 1/2 cups of sugar, 1/2 cup of packed brown sugar and 2 teaspoons of vanilla extract.