It might count towards your criminal record depending upon how your state categorizes the charge of driving without insurance. When you are stopped for a moving violation and you are unable to show proof of insurance, the penalties usually range from suspension of your license and fines to possible jail time. This type of violation is typically added to your driving record and it usually stays on your driving record between 3-10 years depending on your state.
However, some states consider serious traffic violations to be a criminal violation as well. In cases where DUI leads to a fatality, or even reckless driving in states can be considered a criminal offense. So if you are involved in a more serious violation and you do not have insurance, it could be considered a criminal offense. Criminal offenses usually incur more severe penalties and these violations stay on your criminal record permanently. In some states driving without insurance on its own may not be criminal but if it is in conjunction with another offense such as a DUI then it may be and then in other states being an uninsured motorist on its own may be considered criminal and not just a traffic infraction.
You can contact your state's Department of Motor Vehicles for more information about traffic violation, misdemeanors and the penalties you can receive for driving without insurance. Most states have a minimum insurance requirement; you can get affordable insurance quotes for by requesting an affordable auto insurance quote here.