What percentage of babies born are born on their due date?

I had 4 children. Only one of them was born on due date. So I say 1 in 4.
A due date is an average, or a window of time.
Just as 98.6 is considered a "normal" temp, it is really an average. Take a 100 healthy persons. Some never have a temperature over 97.9. Others might always run 99.2. Put them all together, and you get 98.6
In some families women never carry more than 38 weeks, other always "cook" their babies 41 weeks. There are always those exceptions to the rule babies who are born a couple of weeks before their due date, (or after).
The important thing to remember is most of these babies are just fine. Since babies in the womb don't come equipped with calenders, it is usually best to let them come when ready, and not be in a hurry, because of a given date.