The above display panel is 4mm thick. Wow! There are 0.3mm thick panels in development. Double-wow!
OLEDs can also be used for lighting.
For more information, see OLED-Info. When I first heard about organic LED's, I thought "They'll have too short a life to catch on." Oh, whoops!
EDIT: I've just spotted Organic Light Emitting Transistors (OLETs). Oh, Myyy!