Dogs come in all different breeds, sizes and temperaments. The dog bed that is right for a small pampered pooch may not be the best bed for a large working dog. There are almost as many types of dog beds as there are dog breeds. Observe how they sleep, do they curl up or stretch out. Pillow or Cushion Dog Beds - These are the most common dog beds in use. They come in round, square and rectangle shapes and many different sizes to fit any breed. There is a multitude of fabric and color options to choose from.