OLED in mobile phones
At the beginning, there was only PMOLEDs
Back in 2001, we started seeing OLEDs used in mobile phones. The first OLEDs where PMOLEDs, usually small, with one or two colors, and a low resolution. Usually these OLEDs were used as secondary displays. For example see the Motorola Timeport P8767 (2001), LG VX6000 (2003) and the Samsung SGH-E715 (2003).
AMOLED displays are much better displays, with high resolution and great colors. The first phone to sport an AMOLED was the BenQ-Siemens S88, back in 2006. It had a 2" (176x220 pixel, 262K colors). The panel was made by AUO.
The S88 marked the beginning of a trend, and AMOLEDs are being used in more and more phones.
OLEDs in phones today
There are many mobile phones today that have an AMOLED display, from all the leading companies, including Samsung, Nokia, LG and others. Samsung is the leading company, with over 10 new models sporting OLED displays ranging from 2.2" to 3.7". The largest display is on Samsung's new Omnia HD phone (the i8910). It's got a 3.7" OLED with 360x640 resolution.
Samsung see OLEDs as a way to make phones that have superior displays, are thinner, and are more power efficient. In fact Samsung thinks that within 5 years, 50% of new phones will have OLED displays. They have already shipped dozens of different phones with OLED displaying. A couple of their OLED phones, the JET and the Ultra Touch, are enjoying great sales.comprehensive mobile phones with OLED list.
What the future holds
OLED can actually be used to make flexible displays. Within 3-5 years, we'll start seeing bendable, flexible and rollable displays. This will allow mobile phones makers to create radical new designs... Here's a concept phone by Kyocera, that uses a foldable OLED: