What is the best Mind-Mapping application available for free and/or purchase?

With the wide array of free available mind mapping and concept mapping applications available, it doesn't make sense to purchase one of the expensive mind mapping packages. I recommend VUE (http://vue.tufts.edu), the Visual Understanding Environment, an open source application available for Windows, Mac and Linux.

I find formal mind mapping to be limiting in allowing me to think through a problem, and so I shy away from tools that impose the rigid structure of a mind map with a central idea and spokes of nodes built off it, this is one of the reasons I like VUE. VUE does all the basics that most people are looking for but than also contains a bunch of neat features built around presenting from your map, and allowing you to manipulate data feeds from your favorite websites as nodes on a map. It also allows exporting of your map to a PDF outline, which may fulfill your requirement. VUE allows you to attach notes, tags, URLs, files to both nodes and links, and allows building hierarchical stacks of nodes each containing their own nodes and links which can be useful in many cases. It doesn't allow you to export your map to plain text, not sure if this is a blocker for your use case.

I've tried Freemind as well, another excellent mind mapping application, but VUE is just much prettier and easier to use. A long time ago, I tried Cmap but didn't get very far.

I currently use XMind and have an old version of NovaMind, 1.7.

I just got out of a meeting with Mike Kollen, an engineer and online trainer. He was raving about Mind Manager. He said he's tried them all, and bar-none this is the best. He convinced me to check it out.

You don't say what platform you are on, but I am using MindNode on the Mac. There is the free version which has all the capabilities I need. There is also a Pro version which adds things like constraints, cross connections, and hyperlinks. Finally there is even an iPhone / iPod Touch version. The free version is relatively basic, but it more than suits my needs. All of them are at http://www.mindnode.com