I went on a Segway Tour a few weeks ago and can I just say, "These things are a blast." If you purchase one on your own your need to take a more advanced training course, but they are VERY easy for the average Joe to operate. If I can do it, anyone can.
I do remember the CM mentioning that they are not allowed in the parks with the exception of Trained CM's and Segway Tours. In crowded conditions, such as WDW, I could see how they could cause some damage to other visitors although you really can stop on a dime if you had to.