I've known of a few of these for a while and others are new discoveries. It seems the list for these brain storming resources is growing rapidly. Some are purely web based while others have smart phone apps and sync up across devices. It's really a choice of personal preference and they all work a little differently so...without further ado, here's a few =)
MindMeister (iOS, Android, Chrome, Web) - This is a great mind map for collaboration and it is available in the iTunes App Store and the Android Market. You can have 3 active mind maps when you sign up for a free account. *Helpful Tip - Once you click sign up look at the bottom of the site for the FREE account link as it is not featured on their page).
- Mindmaps (Chrome, Web) - I really like the simplicity of Mindmaps and the fact that you do not have to register for an account to use it. To connect ideas you just drag the red dot from one idea to another.
- Lucidchart (Chrome, Web) - Lucidchart works by first dragging the shape you want onto your document. To connect the ideas you drag from any corner of a shape. Lucidchart allows you to collaborate easily with others through a provided link, plus they provide a free upgrade on your account for educators (make sure to click the button on the homepage for this)!
- bubbl.us (Chrome, Web) - My favorite thing about bubbl.us is the speed at which you can add ideas to your mind map. To add a "sibling" bubble just hit the tab key while you have a bubble selected. You can also add a "child" bubble by pressing ctrl + enter on your keyboard.