Could it possible for a young 4yr old child to go ...

Actually, that's not such a far-fetched idea. Only a few years ago, that was the situation in Israel, where I live. When I was 13 (16 years ago), my parents took me to a trip to France and the UK. I was registered in their passports, and didn't have a passport of my own. That means that not only Israel allows for that situation, but that in that time, the French and British authorities allowed me to enter their countries, though I didn't have a passport of my own.

This situation changed, and now every Israeli citizen who wishes to travel abroad needs a passport of his own, regardless of age. But nevertheless, as I said, up until not so long ago, there was at least one country that allowed for children to be registered in their parents' passports. I don't know if there are any countries that still allow it today.

Thats true there is a special form you need to fill out first:

http://travel.state.gov/passport/get/minors/minors_834.html 

Simply put,NO!

Unless he is traveling INSIDE the United States of America he is required to hold a valid passport of his own.

im 15 i used 2 be regesterd on my mums passport and all borders accepted it but now the laws have changed evrybody has to have a passport of their own now nobody can be regesterd to anyone elses passport

In the US, all children (including newborns and infants) are required to have a valid passport to leave or enter the US.