Flexible OLED displays are quickly becoming a reality, and it is expected that starting from 2015 we're going to start seeing foldable and eventually even stretchable OLEDs used in commercial devices. But for really flexible devices, all components must be flexible too.
While flexible batteries are already being developed, another possibility is to use a flexible supercapacitor. Researchers from MIT developed an extremely stretchable supercapacitor based on crumpled graphene paper.
This is still an early device, but the first prototype can be easily be bent, folded, or stretched to as much as 800% of its original size, and can be be crumpled and flattened up to a 1,000 times, without a significant loss of performance.