Can someone have no citizenship

Yes. I heard that people can renounce their US citizenship legally. I do not think that many people have done it, but it's possible. Yes, you can have no citizenship. This usually occurs when you or your country decides to revoke your citizenship. In that case you become "A person without a country"! In practice, renouncing your U.S. citizenship without being a citizen of another country is difficult. During the 1950s and 1960s quite a few people tried it, including the mathematician John Nash (the movie A Beautiful Mind is based loosely on his life.) Nash would go to the American Embassy in Switzerland or France and renounce his citizenship, becasue he didn't approve of US politics, expecially nuclear arms. In some instances he was jailed, and in all cases he was deported back to the U.S., on a new passport issued by the U.S. embassy at the host country's request. The world is not really set up to have citizens who are countryless, unless you are a political refugee. There are many stateless persons in the world. The most common reason for being stateless is that one has been arbitrarily stripped (deprived) of citizenship by a Dictatorship. If stateless persons give birth to children then they too may be stateless, unless they are born in a country where the country of birth confers citizenship, as in the U.S. (and more generally in the Americas). In Europe, for example, children take the citizenship of their parent(s). In some countries, stateless persons who have the status of refugees, enjoy some international protection from their country of residence, which can also issue them with a 'stateless person's passport'. However, being stateless is an unenviable status.