I'm a marine biologist and so don't know a whole lot about the functioning of the human brain but I did some searching on the web and every single information source I came across (most were written by neuroscientists or doctors) debunked the idea that we only use 10% of our brain as a myth. For some examples, see:

http://www.exn.net/Main/JaysBrain/jb-19980128.cfm
http://weber.u.washington.edu/~chudler/tenper.html
http://www.epub.org.br/cm/n04/brainstorming/capacity.htm

No one knew how, why or where this myth got started. There is no known evidence of how much of our brain we actually do use, and most neuroscientists or doctors would be hard-pressed to even figure out a way to measure this. Many of the web pages mentioned the fact that some children who had half of their brain removed early in development (e.g., to prevent severe seizures) grew up to be intelligent, capable adults. However, if an adult were to have half of his/her brain removed, or even a large part, the chances of that person being able to survive would be small, and the chances of that person being able to function normally would be non-existant. So, the brain is very resiliant when we are young, but as adults, most if not all of it appears to be necessary for our survival. Some possible reasons for not using all of our brain is that at any one time we only use a small fraction of it, but over the course of a day or a month we might use 100%; another reason might be that we actively use a small fraction all the time but use the remaining fraction for information storage (like a computer).

For some videos on how the brain works (made available by the National Institute of Health), see:
http://www.nimh.nih.gov/publicat/braincd.htm