MPMoviePlayerViewController is good, but the last commit is a few years ago. I found another solution called "XCDYouTubeKit" that supports iPhone / iPad and iOS7 with full-screen YouTube videos.
You can go to the github page in here and the fully documented tutorial on here
This is what the official developer says on his page:
The only official way to play a YouTube video within the app is the web view and iframe API. Unfortunately, this is very slow and rather ugly, so I wrote this player to give users the best viewing experience.
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