Shou.TV for iPhone and iPad is still in the early development stage.
Shou is a universal iPhone and iPad application that allows you to record your screen, even on non-jailbroken devices. Shou is also a free live streaming site that allows you to broadcast your screen to the world via their online service. The site, http://shou.tv, allows you to stream your iOS mobile device screen in real time with high quality video.
You can register an account for free on their site to get started. They also guarantee that your broadcasts and recordings will be free of ads, as well as preserving your rights and privacy.
If you’re experiencing a 'Black Screen' in your recordings on any device that is not the iPad 2, iPad 3 and iPhone 4, you must turn ON AssistiveTouch in your iPhone or iPad Settings:
General >> Accessibility >> AssistiveTouch.
In addition to AssistiveTouch, fix a black screen, by toggling off Reduce Transparency, in your iPhone or iPad Settings:
General >> Accessibility >> Increase Contrast.
Features
High resolution screen recording up to 1080P @60FPS
Unique and high quality stereo internal system sound recording
Screen mirroring with a web browser, and Apple Airplay
Live stream to https://shou.tv from any iOS mobile device
Known Issues
Black screen for non-jailbroken iPad 2, iPad 3 and iPhone 4.
Can’t edit some recordings, share to YouTube, export to Camera Roll.