When iOS 6 was released two months ago, the native YouTube app went away. Google has since released a YouTube app for the iPhone, but it has yet to release a YouTube player that works with the iPad. After its most recent update, my recommendation for the best all-around YouTube player for the iPad is Jasmine.
A YouTube player for the iPad such as YouPlayer or Video Tube plays videos in a small window while displaying other relevant content such as related videos and comments alongside it. You can, of course, tap again to expand the video to fill the screen (or fill most of the screen, depending on aspect ratio) with these players, but if you like the idea of tapping a thumbnail and having the video automatically expand to fill your iPad's screen, then vTube might hold some appeal. Then again, Jasmine works in this manner, too.
vTube provides a Setting button along the bottom of the screen along with four buttons -- Home, Channel, Category, and Playlist -- that let you browse videos. When you tap a video thumbnail, it expands to play at full screen. For the first few seconds, four buttons are displayed along the right edge of the video: Like, Dislike, Watch Later, and Share. Videos you've tabbed to watch later show up on your Playlist.
vTube embraces simplicity over features. Thus, you will not find an ability to make or even read comments. And vTube does not let you play audio in the background, but it's not alone in this last regard. Jasmine is the only YouTube player for the iPad I've discovered that lets you minimize the app and listen to audio of a video you were watching.
The free version of vTube displays ads; a 99-cent in-app purchase removes them. Before you upgrade, however, I would urge you to try Jasmine or another, more feature-rich YouTube player for the iPad.