Sorry, I'm with Capt on this one. He asked a question about transporting a shotgun and got multiple responses demanding he explain the reason for wanting to do so, which by the way were asked by a guy who's been on the forum barely a month. I understand his frustration and don't think it's fair to say he's looking for a fight when his motives have been brought into question in this manner.
I agree with scsov509. I carry an unloaded shotgun in my vehicle for much the same reasons as Captains1911 espoused. Furthermore, though I have a ccw permit and carry a concealed handgun most of the time, it's been my experience that, when traveling in states other than my own, a shotgun will be more "legal" in many, if not most, jurisdictions than a handgun is and might raise less eyebrows from some police officers.
I am a retired le after thirty years of service and I can assure you that I'm not driving around looking for a gun fight-and I have no idea why some posters have implied that the op might have that in mind when he just asked a simple question.
With regard to carrying the shotgun legally in most states and municipalities, my advice to the op is to not have rounds in a side-saddle and to keep the gun unloaded in a case with the action open.