Mindomo is a cross platform, mindmapping app. You can create three mindmaps for free. However by syncing with your Google Account you can create a .pdf (By hitting print) or .png file of them at any time during the process and keep creating unlimited mindmaps. I recommend having yoru students title their first Mindomo with their name/class. This way you will know who turned in what mindmap.
Integration Ideas:
Planning any Writing Assignment (Obvious, I know)
Create your own study guide
Unit Opener
Reading Comprehension Assessment
Overview of Presentation Slide
Other Tutorials
Check out Teach Thought's Views on MindMap Strategies for Teachers
Step by Step Mind Map creation on Mindomo Slideshare
Examples of MindMaps on Mindomo
11 Inventions that Changed the World