While not exactly a threat to Pixar, Go Animate is a fun online tool that allows students to create their own animated cartoons. It's not the most intuitive interface and the tutorials are virtually non-existent at this point, but it's easy to pick up the basics.
Here's a quick example I made in about 20 minutes.
They're still working out some kinks--it's hilarious that I tried to type "class" and it changed the "ass" part to #$!
It does allow you to record voice rather than text for speech.
For anyone seriously into digital storytelling, the obvious drawbacks of tools such as this and ToonDoo, are the limitations they impose regarding 'camera' angle and framing. You're pretty much stuck with eye level in a square box. I hope, as they evolve and improve, they can move beyond these limitations.