The question in today's Hiibel v. Sixth Judicial District Court decision from the Supreme Court is: Once the police stop a person based on reasonable suspicion that he may be involved in criminal activity, may the police demand that he identify himself (backed by the threat of legal punishment should he refuse, or should he lie)?
The Court's answer: "yes," at least so long as (A) the demand is "reasonably related to the circumstances justifying the stop" (which will almost always be so), and (B) there is no "substantial allegation that furnishing identity at the time of a stop would have given the police a link in the chain of evidence needed to convict the individual of a separate offense" (it's not clear how often this will be so). If condition (A) isn't satisfied, then the person's Fourth Amendment to be free from unreasonable seizures would be violated. If condition (B) isn't satisfied, then the person's Fifth Amendment rights to be free from compulsion to incriminate himself might possibly be violated.
Here are the questions not involved here: (1) May the police stop someone without any suspicion, but just based on an articulable hunch, or a random stop policy, to demand identification? (2) May the police require that the person present some written identification? (3) May the police require identification when the person is driving, or when the person is entering a public building, or in similar contexts? (4) May the police simply ask a person, without the threat of legal sanction, who he is? The answer to #4 is "yes"; the answer to #3 is generally yes, though it depends on the context; the answers to #1 and #2 are still unknown. (UPDATE: Let me clarify briefly my point as to #1 -- as reader Duncan Frissell points out, Brown v. Texas (1979) struck down such random stops when done without any "practice embodying neutral criteria," and when done as part of normal policing. See also Delaware v. Prouse (1979). What is unknown is whether they might be permissible, under the Court's "special needs" cases, when there are some neutral criteria, or when the place is a special location, such as a bus terminal or the environs of some location where security is especially important. There's enough uncertainty in the "special needs" caselaw [which includes cases such as the drunk driving checkpoints] that it's hard to be sure what the result would be there.)