Called a moped, I used to see a few in New Zealand when I was a kid. My Grandmother wanted to buy one, but my straight laced mother talked her out of it. She didn't think it would be right for her mother to be seen riding a motorcycle, so she stuck with her bicycle (which probably didn't impress my mother too much either). My grandmother was born a couple of years before the car was invented, and she never drove one.
Mopeds are quite common in some parts of Europe. In some countries youngsters can ride them on the road from the age of 14.