I'm curious what happens when you do renounce your US citizenship? Are you deported? To where? Whose laws are you subject too? How can you travel anywhere? Can you get citizenship anywhere else?
Edit: Interestingly enough, the US allows it. The Wikipedia page on statelessness says "The United States, which is not a signatory to the 1954 Convention on the Status of Stateless Persons or the 1961 Convention on the Reduction of Statelessness, is one of a small number of countries that allow their citizens to renounce their citizenship even if they do not hold any other." See https://en.wikipedia.org/wiki/Statelessness
Update: the Wikipedia article seems to back that up.