For mindmapping, has anyone used Compendium before? I used it for mindmapping a project, it's rather useful. It's rather flexible and you can create sub-mindmaps easily.
You can also use it for brainstorming sessions and problem solving as a team (project on a screen and let everyone see it). http://compendium.open.ac.uk/institute/download/download.htm Available for Windows, Mac, Linux and free
I started on paper, but there are superb pieces of software for this as well.
iThoughts HD on iPad is excellent. Not sure if they have a desktop client. If desktop is a requirement then check out MindNode which is also very good.