Combine the graham cracker crumbs, granulated sugar, and melted butter. Press this mixture into the bottom of a 9x13 inch baking dish to form a flat layer, then refrigerate it until it's set.
While the crust is chilling, beat together the cream cheese and powdered sugar in a medium bowl until they're well blended. Spread this cream cheese mixture in an even layer over the chilled graham cracker crust.
Next, arrange the sliced bananas and drained crushed pineapple in even layers over the cream cheese layer. Cover these fruit layers with a layer of thawed whipped topping.
Finally, sprinkle the chopped peanuts over the whipped topping and arrange the maraschino cherries on top. Refrigerate the cake until it's completely chilled, then serve it cold.