Used to be that personhood was conferred simply by living and breathing on this planet, at least for most of us. According to the the United States Court of Appeals for the District of Columbia that standard may not apply to the detainees at Gitmo.
Decision document here (PDF warning).
Reading the decision document I think part of the problem for the appellants was that they didn't exhaust other avenues for appeals. However, being told you are not a person has to hurt. Message for the rest of us: Don't get arrested and sent to Gitmo.