National Review, April 23, I copied some part:

In the democratic part of the world, there are also quite large constituencies favoring dual nationality. The one always mentioned in this context is American Zionists, who want to be able to move freely between Israel and the U.S., and to be able to vote, and even stand for office, in both countries. Indeed, the great change in U.S. government attitudes towards dual citizenship occurred in 1967, when the U.S. Supreme Court ruled in the case Afroyim v. Rusk. Mr. Afroyim, a naturalized U.S. citizen, had moved to Israel in 1950. When, in 1960, he tried to renew his U.S. passport, the state department refused, on the grounds that Mr. Afroyim had voted in an Israeli election. Afroyim sued, and eventually won.

In Afroyim v. Rusk the Supreme Court asserted, in effect, that citizenship is a constitutional right, coming under the scope of the 14th Amendment. From then on, the government effectively lost the power to strip you of your citizenship without your consent. To stop being a U.S. citizen you have to take deliberate steps, prove your intent, and formally renounce your citizenship. (Several hundred people do so each year, mainly for tax purposes.) The Center for Immigration Studies has an excellent database of facts and arguments on the subject. Canadian-American dual citizen Rich Wales has also put together a very lucid short summary on the web. To state the present situation very briefly: while the U.S. government does not formally recognize dual citizenship, it does nothing to discourage it; and while Congress might at any time choose to pass laws restricting dual citizenship, there is a strong likelihood that such laws would be struck down on appeal as being unconstitutional.