If a child (under the age of 18) is traveling with only one parent or with someone who is not a parent or legal guardian, U.S. Customs and Border Protection (CBP) strongly recommends that the accompanying adult have a note from the non-traveling parent (or, in the case of a child traveling with neither parent, a note signed by both parents) stating “I acknowledge that my wife/husband/etc. is traveling out of the country with my son/daughter/group. He/She/They has/have my/our permission to do so.”
CBP suggests that this note be notarized. If there is no second parent with legal custody of the child (e..g., the second parent is deceased, one parent has sole custody, etc.), relevant paperwork such as a court decision, birth certificate naming only one parent, death certificate, etc., would be useful as well.
While CBP may not ask to see this documentation when the child enters the U.S., the U.S. is very sensitive to the possibility of child abduction and trafficking, and the child and accompanying adult could be detained if questions arise about the situation. While the U.S. does not require this documentation, many other countries do, and onward travel could be impeded without a notarized permission letter and/or other documentation. (Canada, for example, has very strict requirements in this regard).
This advice applies to U.S. citizens and non-citizens alike. More information can be found on the Customs and Border Protection website.