Not all motor vehicles are required to carry insurance. In CA for example, Mopeds, Motorized bicycles, and certain classes of scooters do not require insurance

Not all motor vehicles are required to carry insurance. In CA for example, Mopeds, Motorized bicycles, and certain classes of scooters do not require insurance and some only require a one time registration fee. Some also do not need to display a license plate. Off highway-on highway vehicles are also a special consideration. In many places, including the whole of CA, you can get points or loose your license for violations on a cycle. DWI on a bicycle is equivelent to DWI in a Car for example. And I've even met someone it happened to. Not exactly something they like to brag about ;).