You need to be connected (obviously) to download, but not to actually watch them once they are downloaded. Easiest way to get them on the iPad is to download directly from the iTunes app (will take a while for movies, they are large files), but you can also purchase them through itunes on a computer and then synch them to the iPad.
Does this process work for rented movies from iTunes as well. I'd rather rent a few movies instead of buy them. Can I rent movies, download them to my computer, transfer to iPad, and watch without wifi?
You could up until the last update which replaced "Videos" with "TV". I just spent a very frustrating two days of flying where I could not get it to work on my ipad because TV insists on having a WiFi connection to see your downloads. Hopefully they will fix this soon, otherwise I will stop buying movies all together. The only reason I buy them is to watch them while flying. I blundered around on my iphone (as opposed to my ipad) until I got it to work from some obscure place. But of course the screen is much smaller. I had to blunder around for half an hour again the next time because it was not at all intuitive how to do it. It did not work on the ipad at all. It used to with the Video app before they replaced it with the TV app.
It doesn't allow downloaded movies without Wifi since Apple "improved" Videos with the new TV. Apparently fixing something that wasn't broke. They also made the navigation more complex. Hopefully, they'll soon fix the fix. 2b1af7f3a8