Brush Ninja
For more than five years now I've been using Brush Ninja to create simple animations. Here's something I wrote about using Brush Ninja a few years ago in an eighth grade class. This video provides a demonstration of how to use Brush Ninja which is free and doesn't require registration. The featured GIF in this blog post was created by using Brush Ninja.
Draw and Tell
Draw and Tell is a free iPad app that has been on my list of recommendations for K-2 students for many years. In this free app students can draw on a blank pages or complete coloring page templates. After completing their drawings students then record a voiceover in which they either explain the drawings or tell a story about the characters in their drawings.