|MindMup is a free web-based mind mapper that seems to allow unlimited maps. It supports multi-user, simultaneous access and can be used without logging in.
It is easy to use, and has easily-found web pages for help, hints and shortcuts.
The appearance is conventional: Bubbles joined by curved hierarchy lines. Relationship lines - the out-of-hierarchy lines connecting nodes in different branches - can only be straight at present.
There are ample keyboard shortcuts (described on pages linked from the map page).
MindMup has the best balance between freedom of movement and avoiding messy maps that I can recall in any mapping tool. Select a topic, hold down Shift, and drag, and the topic moves to where you place it. When released, its children follow and any conflicting branches move aside neatly to leave space. You can freely move any node, not just 1st level ones.
Attachments supported are pages of rich text, images and hyperlinks. Images can be re-scaled positioned relative to the text in the node.
Formatting of the map itself is mainly limited to choice of color for the background of each node. At the same time, progress or other status of a node is indicated by color and the meaning of each color is configurable and can be displayed in a legend panel.
Being browser based, it works on Windows, Mac and Ubuntu. Using Chrome or Firefox is recommended, as it has some limitations when used with Internet Explorer.
MindMup offers three ways of storing your maps: Locally on your computer, in one of the popular Cloud services and on MindMup's own servers. It the time of review they were planning a subscription service (MindMup Gold) allowing up to 1GB of map data (including embedded image files).
MindMup can import and export FreeMind/Freeplane files (.mm) - the hierarchical structure survives the transition either way, but most formatting does not. It can export image files, HTML, tab-indented plain text, and MindMup files (.mup) to your own machine.
There is no explicit multi-maps function, but as all maps have a URL, it is easy to link maps together.
MindMup is open source under the MIT license.
Its developers describe it as 'user-driven' software, and there is a UserVoice page devoted to MindMup.
Roy Grubb reviewed MindMup in detail here: http://www.mind-mapping.org/blog/2013/11/mindmup/ G+