Check this out...some of the Crafty Daisies thought it would be a grand idea if they popped out the decorative wooden piece above the cupboard under the sink where they keep their garbage can and install a 'flap'. Yup, just like in fast food restaurants.
The flap itself is made of a sandwich of thick fabric, which is Velcro-ed in. A scrap of drywall glued onto the back of the flap gives it body and makes it close 'automatically'. Check out the whole trash flap story here.