Driving without insurance falls under the incidence of the Criminal Code and, depending on the state where it occurred, can be a misdemeanor or a criminal offense.
It goes without saying that penalties vary with the seriousness of the offense. Driving at 2am with an insurance that expired at 00:01 that day might be understandable and you could get away with just a warning (it could be that the insurance company has already given you a grace period so it might still count as being insured). However, driving with insurance that expired a month ago is unacceptable.
Penalties are sometimes up to how the officer who pulled you over interprets your “intent to drive”. There are drivers who break the law on purpose and drive without insurance hoping they won’t get caught, and on the other hand, there are people who have genuine emergencies (medical ones for instance) and had to use the car.
First time offenders are charged between $150 and $500. These penalties don’t usually create (or add up to) a criminal record. Repeated offenders will be fined more and, in extreme cases, their license plates will be seized and they will lose their driving privileges. Being involved in an accident makes things even worse: