Lights
Supercapacitor + incredibly high efficiency LED. The light switch is actually an inductive-charging receiver. To switch on the light, you place your phone near the switch. The phone charges the supercapacitor, and the light stays on for a reasonable amount of time.
Application: a picture frame, hung on the wall, where you want to be able to provide spot lighting for the picture but don’t want to run wires to it.