Short answer - No State in the Union requires a citizen to carry identification papers at all times, and no State requires State issued identification when not performing a licensed activity.
Slightly longer answer - Several state specify a person must identify himself when demanded by law enforcement, however, as no state requires identification must be carried, identifying oneself verbally has been deemed sufficient by the Supreme Court.
iRefusal to identify is an offense in a small portion of States, but most States do not criminalize the act of being non-cooperative.
Texas has Sec. 38.02. FAILURE TO IDENTIFY
HTTP://www.statutes.legis.state.tx.us/Docs/PE/htm/PE.38.htm#38.02 Which only applies if one has been lawfully arrested or detained.
MONTANA
Link Removed
46-5-401. Investigative stop and frisk.
...
(2) A peace officer who has lawfully stopped a person or vehicle under this section may:
(a) request the person's name and present address and an explanation of the person's actions
and, if the person is the driver of a vehicle, demand the person's driver's license and the vehicle's registration and proof of insurance; and
INDIANA
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IC 34-28-5-3 Detention
Sec. 3. Whenever a law enforcement officer believes in good faith that a person has committed an infraction or ordinance violation, the law enforcement officer may detain that person for a time sufficient to:
(1) inform the person of the allegation;
(2) obtain the person's:
(A) name, address, and date of birth;
or
(B) driver's license, if in the person's possession; and
(3) allow the person to execute a notice to appear.
As added by P.L.1-1998, SEC.24.
IC 34-28-5-3.5 Refusal to identify self
Sec. 3.5. A person who knowingly or intentionally refuses to provide
either the person's:
(1) name, address, and date of birth;
or
(2) driver's license, if in the person's possession; to a law enforcement officer who has stopped the person for an infraction or ordinance violation commits a Class C misdemeanor.
((A good reason to leave one's license in the car in Indiana ))
COLORADO
16-3-103. Stopping of suspect.
HTTP://www.loislaw.com/livepublish8923/doclink.htp?dockey=8476613@COCODE&alias=COCODE&cite=16-3-103
(1) A peace officer may stop any person who he reasonably suspects is committing, has committed, or is about to commit a crime and may require him to give his name and address, identification if available, and an explanation of his actions. A peace officer shall not require any person who is stopped pursuant to this section to produce or divulge such person's social security number. The stopping shall not constitute an arrest.
(The above list is part of an ongoing project and not necessarily all-inclusive.)