An Internet search for "Mind Map" will lead you very quickly to Tony Buzan - the man who claims to have invented them and who has registered the trade mark of the term "Mind Map" in both the US and the UK. The invention claim is challenged by some, as further Internet searches would quickly reveal.
In Tony Buzan's book "The Mind Map Book", which was co-authored with his brother Barry Buzan, he shows examples of pictorial notes taken by Leonardo De Vinci and Pablo Picasso. It is to be expected that artists would use pictures in their note taking. It is true that spider diagrams and pictorial note taking had existed long before Buzan's Mind Maps but none of these can really be described as Mind Mapping. Tony Buzan's Mind Maps use words pictures and color in an advanced yet simple system of note taking that with can be used by almost anybody and for virtually any application. Although it can be seen where some of his ideas have come from there currently seems to be insufficient evidence to disprove his claim to be the inventor of Mind Maps.
Mind Maps were unheard of until the early 1970s when Buzan brought his system to the attention of the public in a series of television programs titled "Use Your Head". In 1974 he published a book with the same title. The television series and the book also covered other aspects of learning and thinking techniques such as speed reading and memory training. The book eventually became part of a set of books called "The Mind Set" which also includes two books about memory techniques, the previously mentioned "The Mind Map Book" and his earlier work "The Speed Reading Book" which was first published in 1971.
Since his rise to prominence in the 1970s Tony Buzan has continued to promote Mind Maps through his company "The Buzan Organisation" and more recently through the website "ThinkBuzan" where it is possible to download a trial of "iMindMap 5"; the current version of the official software package for the creation of Mind Maps.
According to the "ThinkBuzan" blog entry for 20th September 2011 Mind Mapping is used by over 250,000,000 people worldwide. Even if these figures are somewhat exaggerated it is still a firm recommendation for Mind Maps as a natural way to organized thinking which most closely parallels the way our brains work.