From telling personal stories to narrating instructions (e.g. how to cook a meal) or historic events, there are plenty of tools to choose from.
Narrable is an App with which you can upload an image and record a brief message (a bit like Fotobabble) . However, it is Muvizu which has really captured my imagination for storytelling.
Muvizu is animation software which creates 3D characters and is free to download. There is a wiki where you can find hints and tips when using Muvizu, including a tutorial page.
For MAC users, there is also a video explaining how to use Muvizu:
Creating animated stories makes a great project for students, letting them re-mix what they have been learning in different subjects while adding their personal touch.