I ask because I was born in the US and am a US citizen. However, if I want to move to another country I don't want to give up my US citizenship. If I move, I want to pick a country where I can have dual citizenship.
To answer your specific question, you cannot lose your US citizenship unless you explicitly state intent to relinquish your citizenship. From Advice about Possible Loss of U.S. Nationality and Dual Nationality:
Section 349 of the INA (8 U.S.C. 1481), as amended, states that U.S. nationals are subject to loss of nationality if they perform certain specified acts voluntarily and with the intention to relinquish U.S. nationality.
It goes on to say that a consular officer will ask whether the person intends to relinquish U.S. nationality:
If the answer to the question regarding intent to relinquish nationality is yes, the person concerned will be asked to complete a questionnaire to ascertain his or her intent toward U.S. nationality. When the questionnaire is completed and the voluntary relinquishment statement is signed, the consular officer will proceed to prepare a Certificate of Loss of Nationality of the United States. The certificate will be forwarded to the Department of State for consideration and, if appropriate, approval.
This page makes it clear that the default position is that U.S. citizens do not intend to give up their U.S. citizenship. The only exceptions are when an individual:
- formally renounces U.S. nationality before a consular officer;
- serves in the armed forces of a foreign state engaged in hostilities with the United States;
- takes a policy level position in a foreign state;
- is convicted of treason.
You may acquire any other citizenship (according to the laws of the other country of course) without affecting your U.S. citizenship.