Ask HN: What are some of the mind mapping and outlining apps you like the best?

I am trying to find a tool to create/maintain mind/concept maps and outlines I would love and use actively. No luck so far. I would appreciate everybody to share recommendations.

Free (at least for a limited number of users and a limited number of documents) collaborative mapping is appreciated yet not mandatory. An option to download a document as a file is a must. All documents must be private unless I actually choose to publish them.

Recommendations targeting any of the popular platforms (including mobile, web and PC) are welcome, so are both free and commercial apps.