You can be arrested for refusing to identify yourself to a police officer, and you can certainly be arrested for driving without ID, but you aren't required to carry papers simply to walk down the street.
We like it that way.
24 states have such a statute. My new home state, California, has none.
I find if you clearly & politely ask what you are legally required to do, most cops will honestly tell you.
Case in point: http://www.seattlepi.com/local/418746_video.html
You do have to identify yourself; presumably, if you're carrying ID and refuse to show it simply to be a dick, you're inviting trouble. But you'd have grounds for a complaint if you were detained and then arrested because you genuinely didn't have an ID card.