Someone mentioned MindMeister, which I’ve used before. I knew I’d had a play with something else, though wasn’t sure what. Googling found not only what I was looking for, Mindomo, but another tool that looks very promising. Judging by the review I found by Steve Castledine – and the home page, I think that it’s worth investigating further, much as I don’t really “get” mindmapping.
Kayuda have a mindmapping tool that appears to be a front end to a wiki. I’ve only had a small play so far, and it seems to like IE better than Firefox.