During Google's financial results conference call, the company's CEO Larry Page discussed the opportunities in mobile phones. The company bought Motorola Mobility and is expected to release new phones with new technology soon. Page hinted at unbreakable phones ("when you drop your phone, it shouldn't go splat") and said that battery life is still a huge issue. Hopefully Motorola will indeed incorporate unbreakable plastic-based OLED panels in their upcoming device (some say it'll be called Google X).
Motorola already uses OLED panels in several of their mobile phones, including the relatively new RAZR i, RAZR HD and RAZR M. Most of these Motorola's OLED phone sport Super AMOLED Advanced displays, which are 25% more power efficient compared to other OLEDs (according to Motorola's marketing, anyway). This is probably due to the fact that Motorola's displays are one of the few Samsung OLEDs that use green phosphorescent emitters, and may be the reasoning behind Page's "battery life" comment.
Google themselves have opted for OLED displays in their Galaxy Nexus, Nexus S and Nexus One phones. Their latest one, the Nexus 4 (made by LG) uses a 4.7" 1280x768 IPS display (probably made by LG Display).
During CES Samsung officially launched their YOUM AMOLED displays - plastic-based, shatterproof flexible OLEDs. Samsung didn't commit to any production schedule, but it seems that they are getting closer and closer to mass production. The company showed several phone prototypes including one with a 5" curved OLED panel.
LGD is also on track to start mass production of plastic based flexible OLEDs, in H2 2013. The capacity will be "very limited" and they expect to be able to support just one or two customers.