To be honest, I was very sceptical of them at first as well; however, now I have my mind mapping software load at start-up - that is how much I need it. I put everything related to my ideas in it: links, notes, images, videos, pdf's, etc. One thing that you have to be careful of is that the maps for ideas can quickly grow to become huge, and I have now found it more beneficial to split large maps into smaller ones and just link through to them. They are also really useful if you have more than one idea on the go. Good software will allow you to set-up different styles too; this can be useful for simple flow diagrams.

Mindmaps have been an invaluable tool for me to organize my thoughts. They're less restrictive than simple down-the-page tree hierarchy notes, more understandable at a glance, and keep ideas connected. They've been most useful when I've been trying to grasp really big ideas that take multiple lines of thought.

It's not a tool for providing fully-detailed notes. They've been most useful for helping people who already know the subject matter better understand it.

Personally, I find the idea of concept mapping to be much more 'useful' than mind mapping as I don't like having 1 big idea stuck in the middle of a map. However, to organize your thoughts in a not strictly linear format, there are worse ways than mind maps.

Also, having the ability to expand/collapse branches of the tree make it fairly useful for organization of projects or for GTD systems. This is not something easily mimicked with other note taking/text tools.

"The thing is, I keep stumbling into people and books who swear by it and sing all sorts of praises."

Religious people do that do but they don't impress me.

For what it's worth, I see it as nothing more than an outline that pines to be a spider chart. It's foolish to say one form of personal organization is better than another if your aim is to convince other people of the same thing. Do whatever works for you.

In my case, so long as I have things written down, I'm good.

I use it for brainstorming. It allows me to effectively operate in both "sparking off lots of quickly-forgotten ideas" and in "elaborating in depth" mode.