From the map on http://www.opencarry.org/
Arizona is one of our "Gold Star" open carry states. There is complete state preemption* of all firearms laws, open carry is common and law enforcement is well educated as to its legality.
*Complete preemption of firearms laws except localities may still limit firearms possession in parks or preserves to persons who possess a concealed weapons permit.
I live in Mesa, and OC is quite common. I've seen it on motorcycles on the street, seen it in the bank, in the junkyard, in the eye doctor's office, and just out and about in general. Last time I called a tow truck, the driver was OCing.
With 400,000 people in our little "suburb of Phoenix," it's not like you're going to see it on every corner, but it is common and it is commonly accepted.
No permits, no registration; all you need is a gun and a holster.