Mind42 (as in For Two) from IRIAN Solutions (I think from Germany) does this and it’s a beautiful implementation – similar to Geni‘s geneaology approach.
It’s got some nice basic icons – a VERY easy to use interface and wow! The Collaboration totally rocks and to make matters worse for other Mind Mapping tools, it imports and exports Mind42, FreeMind and Mind Manager files.
I had created a fairly advanced MindMap in Mind Manager and was able to open it without a single problem with Mind42. However, it was unable to open my map that had linked submaps in it.
Some things I didn’t like: the direction is always left to right – I can’t go down or around or so it looked like. You can do this by adding multiple nodes but it wasn’t completely intuitive.
I also had some trouble selecting the nodes correctly every time but the collaboration totally rocks – a colleague and I were editing live just like we do in Google Docs with chat and all.
Check out my sample published map here: Sample MindMap