There has been a revival of interest in animated GIFs since you can make some fun stylized animations with them. Some of the more recent stuff is pretty interesting, which is probably why the Cinemagram app was just released for iOS devices. It allows you to easily create animated GIFs and share them directly from your iPhone, iPad or iPod touch.
Cinemagram converts short film clips into a single, animated image. It also offers special filters and photographic effects that can be layered onto the resulting animations. You can even select only a part of an image into a GIF, making it look like a video is embedded in a still photograph. Here are a couple of examples produced with the app: