What I have learned from this thread:

a) Don't trust what others say about citizenship rules. There are a lot of old wive's tales, outdated information, misunderstandings of the rules. Do your research into the laws of the countries that you are concerned about.

b) Do not only be concerned about your own citizenship. Find out what the rules are that apply to your children. It seems that in some circumstances you may need to take certain actions to ensure that your child can establish their citizenship. For example, it is not clear what happens when a child is born outside the U. S. to one American citizen who has never resided in the United States and one non-American citizen. It appears, based on the Child citizenship Act of 2000 that they can acquire citizenship by being admiited as a lawful permanent immigrant before the age of 18. This is automatic. Alternatively, if they are admitted to the U. S. before they are 18 under non-immigrant status, they can establish their citizenship by applying for a certificate of citizenship. What is not clear, is what happens if they never visit the U.S. before they are 18. It seems worthwhile for children of one American parent to take positive steps to establish their citizenship rights to avoid this situation.