In most states...yes, you must present ID if it is requested by a police officer.
As a blanket statement, that is incorrect.
I am not a lawyer, and this is not legal advice, but I was a legal officer during part of my Navy service. As others have pointed out, the police can legally demand some form of identification from you regarding certain activities such as driving (driver’s license). But in general, the police cannot legally demand that someone identify himself or provide a form of identification unless they have a suspicion the particular individual is engaged in wrongdoing.
For a Terry Stop, the officer needs articulable facts that support reasonable suspicion. Such facts include your presence at the scene of the crime, that you fit a general description of a suspect, that you are engaging in suspicious activity, and a whole host of other things. The Terry Stop is where the stop-and-identify statutes come into play, but even there I’m not aware of any that require you to carry a form of identification, unless whatever you’re doing at the time requires some sort of license, or you are an immigrant (lawful permanent resident but not a citizen) or a non-immigrant alien.
The officer might begin by talking with you in an “encounter,” which is considered a voluntary exchange between you and the officer and is perfectly constitutional. If something you say or do creates suspicion in his mind, he can then turn the encounter into a Terry Stop. For example, he might ask you, “Do you live here?” You reply, “No, I’m visiting with my Aunt and Uncle.” He then asks, “Where do they live?” You say, “I don’t know.” He then asks, “What’s their phone number?” You say, “I can’t remember.” You have likely failed the encounter by giving implausible answers and have given the officer the reasonable suspicion he needs to conduct a Terry Stop.
On the other hand, if instead your first response is something like, “I don’t want to talk with you. Am I free to go?” and he says, “No,” he will need some other basis (under a “totality of the circumstances test”) for reasonable suspicion before he can legally turn the encounter into a Terry Stop.
All of the above deals with what can legally happen, which was the OP’s question. “No” is the correct answer to the OP’s narrow question of “Do you have to show ID to the police just because they ask for it? Not in response to a traffic stop or any other possible infration, just because they ask?”
But what about what can illegally happen? Can a police officer lie about the basis for reasonable suspicion? Sure. He puts himself and his department at risk for doing so. How big is that risk? Depends on how far he pushes things, how much harm you suffer, how willing you are to do something about it, and the likelihood you can prove your case. Even then, you are not legally required to provide a form of identification; whether you can prove his request was not legal is a different story.