YouTube will start to show this warning video and next month "v2 API calls except for comments and captions will receive 410 Gone HTTP responses".
Unfortunately, there are still devices that won't be updated, so many people will no longer be able to use the built-in YouTube apps from Apple devices that run iOS 5 or earlier (iPhone 1st generation, iPhone 3G, iPad 1st generation), Apple TV (1st and 2nd generation), Google TV 2 or earlier, old Smart TVs and game consoles. Devices affected were "manufactured in 2012 and earlier, including Sony TVs & Blu-ray Discs, Panasonic TVs & Blu-ray Discs, older iOS devices, and devices running older versions of Google TV."
Mobile devices and smart TVs have browsers, so users can still watch videos at m.youtube.com or youtube.com. For Apple TV 2, you can still watch YouTube videos using AirPlay.