In many countries young children are allowed to ride pillion on a motorcycle, depending on the child's age and the engine displacement, provided they are carried in a suitable child safety seat. Now, we don't like to be hung up on ages, but as soon as the little man or woman feels comfortable with it, a ride on a motorcycle can sure be lot of fun.
A well made child seat contributes to a safe ride anyway and some can even be adjusted to accommodate for the growth of the little passenger over time.
Do we still have to remind people that a children's seat is not enough to achieve a minimum safety level? Fitting them with appropriate clothing and helmet of the correct size are minimum requirements on the motorcycle, no matter the make and model, or the distance of the ride.
Just to be clear: it may not be legal in your country to carry children between the ages of three (3) and eight (8) years of age on any motorcycle, so check your local rules and regulation beforehand.