The University of Tokyo has developed a concept controller that allows you to control a pointer on a phone screen without having to touch the screen.
You can see the concept in the video above, which demonstrates moving a pointer around, using a virtual keyboard, and zooming around a picture and even painting in 3D. The camera's able to sense distance away from the lens, so you can briefly tap towards it in place of clicking on a real touchscreen.
While this remains a concept for now, and may not prove as easy-to-use as a regular touchscreen for most tasks, there are definitely use cases for it. For example, it'd be easy to see an idea like this implemented for kitchen gadgets - which you might not want to touch with mucky fingers while you're cooking.
Can you think of any other situations when you might want to control a screen without touching it directly? Tell us in the comments.