From basic all-accessible (students, PR folks, etc) multi-person live brainstorming dashboards TO feature-rich, techy diagram creation tools.

Basic Mind-Mapping Tools

(1) ImaginationCubed – awesome looking, simple to use, live brainstorming tool. Invite your partner and share single dashboard to create mind maps. Draw, add objects, type, etc.

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Features: Demo

• live collaboration
• send maps by email
• replay your steps
• save/print maps
• background grid on/off

(2) Bubbl.us – lets you quickly create custom bubble mind maps and share them with colleagues for further refining.

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Features: Demo

• create/save/print/share/collaborate on maps
• embed maps elsewhere (blog, web profile, etc.)
• export maps as XML, HTML, or as image (JPEG, PNG)
• interactive Drag’n Drop interface
• keyboard shortcuts, mousewheel zoom

(3) Mind42 – cool mind mapping tool for creating highly customizable organization charts. Each chart node can be colored, converted to an image, supplemented with a custom icon, link, attachment and more.

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Features: Demo

• sharie and collaborate on notes
• embed maps elsewhere
• print maps
• integrated live chat (Google Talk)
• keyboard shortcuts
• Drag’n and drop interface
• export maps (as Freemind, Mindmanager and RTF)

More Powerful Mind-Mapping

(4) Mindmeister – slightly more flexible alternative to the above mentioned mind42: more styling/formatting options, more diverse collection of embeddable icons, provides handy sidebar next to the mapping dashboard, and more.

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Features:

• free account is limited to 6 mind maps
• share and collaborate on mind maps
• print maps
• integrated Skype conference call
• embed maps into your blog or website
• drag’n drop interface
• keyboard shortcuts
• import maps (from FreeMind and Mindjet’s MindManager) / export to an RTF or a GIF image

(5) Mindomo – feature-rich mind mapping tool. Probably the most comprehensive one, check out screenshot and demo below.

Features: Demo

• free account is limited to 7 private and an unlimited number of public maps
• share and collaborate on maps
• keyboard shortcuts
• drag’n drop interface
• import MindManager and FreeMind type maps / export to maps to TXT, MMAP, RTF, PDF, JPG, GIF and PNG formats
• print maps

(6) Gliffy – extremely powerful techy-oriented diagram creation and collaboration tool, create anything from basic flow-chart diagrams to well-documented troubleshooting guides.

Features: Demos Video / Trial

• free account is limited allows you to 3 private and unlimited number of public diagrams
• share and collaborate on mind maps
• embed maps elsewhere (blog, wiki, etc.)
• export mind maps as SVG (Microsoft Visio, Adobe Illustrator, and Macromedia FreeHand)
• interactive drag’n drop interface
• print maps
• map edits history (instantly revert map to earlier version)
• keyboard shortcuts

[UPDATE] Awesome related links contributed by Vic

• Bubble-Mind
• Kayuda (concept mapping more than mindmapping)
• Mapul
• Comapping (kinda rigid, forces left-to-right mapping)
• Webofweb (prob. the oldest still surviving – mayomi came first but has sunk from sight)
• Glinky

And in the area of more general diagramming tools, there’s

• FlowChart
• CumulateLabs (Cumulate Draw)