By default, you can’t download YouTube videos on your iPad but using YourTube HD you can download or save YouTube videos on your iPad and watch then later.
YourTube HD is an application for iPad that let you download YouTube videos on your iPad. YourTube HD is available on Cydia store but for this you must have a jailbroken iPad.
If your iPad is not jailbroken and want to jailbreak your iPad:
Windows: Jailbreak iPad with Spirit ( for iOS 3.1.2, 3.1.3, or 3.2)
YourTube HD costs $2 and you can download it from Cydia Store to save / download YouTube videos on iPad.
Is that a free iPad application to download youtube videos?