Researchers and doctors say that between 30% and 50% of children with ADHD or ADD grow out of it by the time they are adults. I am going to step out on a limb and say that no one actually outgrows ADHD.  I would prefer to say that about 30% to 50% of people with ADHD reach a point where they no longer need medication.

This happens for a few reasons. 

First, a person simply learns to deal with ADHD and no longer needs assistance from medication. The mind tends to learn new ways of doing things in order to accomplish its purpose.  Sort of like a rat in a maze.  Given enough time they will find a solution.  The human brain will do the same thing given proper motivation.  At least that is my experience.  People also tend to teach themselves ways to outsmart the problem.

Second, a persons environment changes to where the problem is not a problem anymore.  In many cases it becomes a strength.  For example, lets say you have a person that is very hyperactive.   Make them sit though a philosophy lecture for a couple of hours and you have a problem.  However, put them on a racquet ball court and the problem seems to go away.  The person did not change, the environment they were in did.  When a person goes from a classroom setting to say a work setting where concentration is not as crucial then ADHD may not be an issue at all.   Also, as you get older the hyperactivity problem normally lessens or goes away naturally. 

Thirdly, the symptoms can actually become less severe over time.  As a persons body chemistry changes it is possible for attention deficit symptoms to lessen.  It does not go away but just becomes less of an issue.