A GUN!
Is that really a must have item when touring over in the US?
Not most places, but some, when you end up NOT where you were planning on going, for some reason.
Ever needed to use the gun to get out of a sticky situation, while touring?
Yes. But this being the Internet, that's all I will say here.
ABSOLUTELY anywhere I go plus a backup on or off a bike.
Not a bad plan, however I have usually found one is enough. Deep concealment is part of it, to be sure. It's not about shooting, but about 'escaping' a situation for having had it when needed. Keep in mind: I grew up my High School years in Chicago (I was jumped and beat up 3 times in the Chicago riots of the late 1960s), after growing up as a youngster in mostly the countrysides of this great nation.
How do you address the varying laws from state to state?
By knowing them, being prepared, and [lately] insured as well. I actually buy and carry the annual publication (in paperback, folds up well) that denotes them, and plan my trips accordingly. On some occasions this has changed my itinerary, but never my destination.
Enjoy the ride and steer clear of the inner city of large metropolitan areas would be my advice. Pay attention to your surroundings, and if a place doesn't "feel right" then simply ride on to the next stop.
Good advice! That's part of what went wrong for me on that particular day, but 'twas in a small town that turned out to have a bad rep (which I knew nothing about).