It depends. Generally speaking, if you are stopped on the street by police for a "consensual interview" you are not obligated to show identification. There is no law requiring U.S. citizens to carry any identification. However, identification is required if you drive a vehicle or fly with a commercial airline.
"Stop and Identify" Laws
Many states now have "stop and identify" laws which requires that a person identify themselves to police when the police have reasonable suspicion that the person has engaged or is about to engage in criminal activity. Under the law, if the person refuses to show identification under these circumstances, they can be arrested.
Determining If You Are Under Reasonable Suspicion
How will you know if the police are asking you for ID because you are under "reasonable suspicion?" Politely ask the officer if they are detaining you or if you are free to go. If you are free to go and you do not want to divulge your identity walk away. But if you are detained you will then be required by law (in most states) to identify yourself or risk arrest.
The Pros and Cons of Showing Your ID
Pros: Showing your identification can quickly resolve cases of mistaken identity.
Cons: In some states if you are on parole you could be subjected to a legal search.