To clarify, you can't be convicted in the US for simply not carrying ID. You can still be effectively arrested and detained for a while with little or no recourse in many places.
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.
Case in point: http://www.seattlepi.com/local/418746_video.html