There are many reasons the displays in all of your devices are as flat as a pancake, including the simple fact that curves result in distorted images that are hard to correct. But taking a design cue from nature, researchers at Disney have created a curved display that manages to avoid warping altogether.
Instead of RGB pixels, the display is made up of light channelling fibre optic-like tubes arranged in what's known as a fibonacci sequence -- which occurs naturally in nature. (Think of how the seeds on a sunflower are arranged.) Light is projected into the flat end of the display, and forms an image on the curved, bulging end that doesn't look stretched or distorted. The technology even supports touch interactivity using an infrared camera.
As for practical uses? Since Disney's behind the research the obvious uses are as a way to enhance the audio-animatronic characters in its parks. But it could eventually even see uses in futuristic-looking vehicle dashboards, or even as a computer interface device -- think trackballs but with additional visual feedback.