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) [NO LONGER WORKS] 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: [NO LONGER WORKS] 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