FlixAPix (free) is an innovative app that lets you take a pair of photos and add an interesting transition between them. In-app purchases offer additional transitions. Photos can be captured live from within the app, or you can import from your camera roll.
You can sign up for a free account, but it isn't required. All the rendering is done off your device on a remote server. With an account a space is created with all your animations. Without an account, they are still there but you may have to search among all the other unregistered people creating animations. Your photos remain private and are not viewable to others.