In response to Chica's comments re children born to a US citizen but born outside of the US -

I'm a US citizen and was married to a British chap and we lived in Sydney, Australia when my daughter was born. Register a childs birth at all three consulates!

That way you and the child are covered in all circumstances. If you travel with a youngster they can be on your passpost with this having no effect on the dual (triple in my daughter's case) citizenship.

Depending on the citizenships involved - at some point the child (now an adult) will have to opt for one passport ....

Regardless - check any and all current rules and regs for every country involved shorty before the childs birth.