Quote from piezoe:
Apparently the circumstances dictate whether one can be a citizen of more than one country at a time. It was true, and I am assuming it is still true, that for an immigrant to be given US citizenship they must formally renounce their allegiance to all other countries. This was part of the swearing in procedure to become a US citizen, and I would guess that it still is. In other words, persons granted U.S. citizenship by this procedure may not legally be a citizen of any other country.
It indeed used to be the case in the US that you couldn't hold dual citizenship (except in certain cases if you had dual citizenship from birth or childhood, in which case some Supreme Court rulings -- Perkins v. Elg (1939), Mandoli v. Acheson (1952), and Kawakita v. U.S. (1952) -- permitted you to keep both). However, most of the laws forbidding dual citizenship were struck down by the US Supreme Court in two cases: a 1967 decision, Afroyim v. Rusk, as well as a second ruling in 1980, Vance v. Terrazas.
The Constitution says nothing explicitly about dual citizenship at all. Indeed, in its 1967 ruling in Afroyim v. Rusk, the Supreme Court used an argument derived from the 14th Amendment to the Constitution to affirm a right to dual citizenship
Rules against dual citizenship still apply to some extent -- at least in theory -- to people who wish to become US citizens via naturalization. The Supreme Court chose to leave in place the requirement that new citizens must renounce their old citizenship during US naturalization. However, in practice, the State Department is no longer doing anything in the vast majority of situations where a new citizen's "old country" refuses to recognize the US renunciation and continues to consider the person's original citizenship to be in effect.
It was once the case that a naturalized US citizen could lose his citizenship by remaining outside the US for an extended period. However, this provision was invalidated by the Supreme Court in Schneider v. Rusk (1964) and was repealed by Congress in 1978.
The official US State Department policy on dual citizenship today is that the United States does not favor it as a matter of policy because of various problems they feel it may cause, but the existence of dual citizenship is recognized (i.e., accepted) as a fact of life. That is, if you ask them if you ought to become a dual citizen, they will recommend against doing it; but if you tell them you are a dual citizen, they'll almost always say it's OK.
