Popplet: Simply the BEST iOS brainstorming app
While I haven't (yet) had the opportunity to test Popplet with my students, I can not recommend this app highly enough - based on my extensive reviews of iOS (iPad) brainstorming / mind mapping apps.
Popplet works well on the web, however, it's best application is on iOS devices, particularly iPads. It is an intuitive, and extremely visual tool, and works well in the classroom.
The free Popplet on iPad is limited slightly; however, I believe this is worth paying for - particularly if you are interested in encouraging student thinking and group collaboration in the classroom
How I Use It
Brainstorming / mind mapping - for personal use only at this stage