For some time there was a Minecraft iPhone app available in Apple’s app store. However, that’s not an official app by Notch (original developer) and his team and was pulled for various reasons. Still, an iPhone app would definitely rock!
A bunch of Minecraft clones popped up recently (always, when something has success there are copycats) including an iPhone app. The creator of the iPhone app Minecrafted didn’t actually want to release it yet without asking Mojang Specifications (the company Notch created) first.
Image: Minecraft iPhone App
Notch said that clones are allowed, but should not be labeled as an official Minecraft app/client. He also added that new ideas and improvements are more welcome than simple 1:1 clones.
Maybe there will be an official or unofficial Minecraft app in the near future, but for now we can only run it on mobile devices like the iPad!