A Japanese consortium of 13 companies and institutions are working on developing some super-thin and flexible LCDs. They use plastic instead of glass substrates, and layering them for displaying color.

So far, this consortium has a 3.5 inch LCD that is 0.49mm thin and weighs 7 grams. They expect to have a more advanced version by 2012, but who knows what year mass-produced thin and curved LCD screens.

Source