The Blank concept phone by Chris Kujawski offers a full OLED display screen on the front body. Similar to iPhone and LG Prada phone, the full LCD screen has different input screen that will help you without the physical keypad.

According to the designer,

Utilizing a flexible Organic Light Emitting Diode (OLED) touchscreen, BLANK is
based on the principle that the device that you carry with you most often should
reflect your personality as much as the clothes you wear, car you drive or music
you listen to. Since those may evolve from season to season, your phone needs to
accommodate that.  By providing you with a 'blank slate' in the form of the OLED
touchscreen that wraps the entire front of the phone, you are free to express yourself
in any number of ways visually by downloading static or even kinetic skins that make your phone come to life, just the way you want it to.

Source via unwiredview