Motorized scooters do require the driver to be at least 16 years old, wear a helmet, and carry a drivers license. However, they do not require the driver to have registration or have license plates on the scooter.
It depends on which state you live in. I live in Pennsylvania and to drive a scooter, you'll need to be at least 16 and have either a motorcycle license or a motorcycle endorsement on your license. You will also have to have it registered and you will need insurance.
In the state of Maryland, at this time, you need a regular, valid driver's license to drive a scooter that has a motor of 50cc or lower. A scooter that is more powerful will require you to obtain a motorcycle license.