No license is required to own rifles, handguns or shotguns (as defined in law) at the Federal (U.S.A.) level, but local restrictions unfortunately can and do apply. We are fighting against these local restrictions (my state has few to no restrictions) and several local laws have been overturned or superceded.
In my state, land ownership only negates the need to purchase certain licenses. Daily limits still apply. For instance, the current cottontail rabbit limits are 10 per day, 30 total in possession. Any landowner in possession of more than 30 rabbits would be in violation of the law.
We only rarely hear of daily/possession limit law being enforced, and most of the time the enforcement is made against those truly stupid enough to openly break the law.
Considering how much of each game type is allowed, simply eating what you've hunted is an easy way to stay within the limits of the law.
I have a daughter. I tell her, "911 is what you dial after you're raped. 1911 is what you should have before they try."