In most states if you are hunting indigenous wild game you need a hunting license no matter where you are shooting/hunting, even private land. Most state laws designate that all indigenous wildlife are the property of the state no matter where the animals reside.
If you are hunting non indigenous species than they are usually not covered under existing game laws and most times hunting those animals is not governed by any seasons or bag limits,,, but you may still be required to have a license on you while hunting them. The best course of action is to do just what Gene said,,,, check with your states game authorities for up to date licensing information.
Jeff