Enter Jasmine, a YouTube app for both iPhone and iPad that may just be better than Google's offering, if nothing else, it's the best option for the iPad. Jasmine was created by Jason Morrissey, who is best known for developing the Alien Blue Reddit app for iOS, which was so good that it has been made the official Reddit client.
Jasmine includes nearly all of the functionality you would expect in a YouTube. You can easily search/browse for videos, as well as access your playlists, viewing history, favorite videos, and subscriptions. The app also has some extras, like an easy toggle for night/day mode, and options for video playback, appearance, parental controls, and more.
If you want to try out Jasmine, it is available for free in the iTunes App Store.