This app goes in the "I can't believe you can do this on a iPad" category. Animation Desk (U.S. $4.99) lets you create freehand animations using a generous set of drawing tools and brushes. If you have any artistic ability at all, you can create animations that look professional. The interface Animation Desk presents looks similar to the tools an animator would use in the physical world. Make your drawing, add a new page and redraw with the changes. You can make really good looking animations for business presentations, for animated e-cards for friends, or just for your own enjoyment. When you're done, you can upload to YouTube or share your work on Facebook.
Other nice features are the ability to add sound effects, and there are multiple frame rates, from 3 FPS to 24 FPS.
I gave Animation Desk a try, and without any drawing ability, I created a passable animation with some moving stick figures. Frankly, it exceeded my expectations. If I have any criticism of the app it is that when you first turn it on you see an animation pad, some icons, and some buttons, but I didn't know what to do first. Happily, there was a drop down menu with excellent help, and some videos, but the app needs help marked on the main screen. Users should not have to search for assistance, as when you first start the app the array of features and icons is bewildering. Animation Desk has some in-app purchases, with things like pre-drawn Xmas elements, but I don't think the add-ons are a necessary requirement.
You can get more info on Animation Desk at the developer website, with some example animations that are pretty impressive.
I'm amazed at what can be achieved with this app. It's bargain-priced, and there is a version for the iPhone as well. Animation Desk requires IOS 5 or greater. There is also a free lite version if you wish to try the app without risk.