According to new rumors, Samsung plans to release a smartphone in 2014 that will feature a three-sided display. This is a YOUM OLED display that wraps around the edges, probably similar to the prototypes the company showed at CES 2013:

A prototype curved OLED displayYOUM phone prototype, CES 2013

According to the rumors, the phone will be released in 2014 (probably the second half of the year). Samsung hasn't decided yet whether this will be a Galaxy Note phone, or a Galaxy S one, or an altogether new class of phones.

Currently Samsung produces 5.7" Full-HD flexible (plastic-based) AMOLED displays (as used in the Galaxy Round). It's likely that the 3-sided display will have a different resolution -and size - as the display is actually wider than usual. The idea with the display on the side is that you can show notifications, or even use the area for soft-buttons UI.

Kyulux - Hyperfluoresence OLED emittersKyulux - Hyperfluoresence OLED emitters