LG 40UB8000 1.9" depth - not sure if this is available yet
[Link: lg.com]2012 Samsung UN40ES6100 40-Inch 1080p 240 CMR Slim LED HDTV (Black) - Old, but you can probably find one - 1.8" or 1.2" depth (probably because of the power cord) (I found 1 spec that says it is 30.7 mm)
[Link: amazon.com]Not sure why there are no small OLEDs