The idea that a human beings only use 10% of their brain is often mentioned by motivational speakers and various self-help gurus. It is a great explanation to explain past failures with only one caveat: it is completely false and the origins of the concept seem to be based on outdated science. If 90% of your brain was removed, you would cease to function.
Neurologists that have studied the brain have used modern imaging techniques such as fMRI (functional magnetic resonance imaging) and PET scans (positron emission tomography) to monitor brain activity. Many different studies have demonstrated that a wide variety of locations within the brain are used. Also, some tasks are highly specialized and are controlled by very localized portions of the brain while other complex behaviors utilize many different parts of brain at the same time.
Nevertheless, what does seem to be true is that human beings often use LESS than their full mental capabilities due to sloppy thinking, ingrained habits, and static world views. Almost everyone has the potential to increase their overall creativity and problem solving abilities.
For a much more detailed account on this myth, including more on the cultural history, see the following book chapter:
B.L. Beyerstein, Whence Cometh the Myth that We Only Use 10% of Our Brains? in Mind Myths. Exploring Popular Assumptions about the Mind and Brain edited by S. Della Sala, Chichester: John Wiley and Sons, pages 3-24, 1999