It really depends on the gun. I have a few different carry guns, depending on the situation. I have a couple of single-action autos* that I carry "cocked and locked" with a round chambered, and the gun holstered. There's not a chance I'd carry a 1911 un-holstered in that condition, even though it has enough safety features it would be highly unlikely to have an AD.
That said, the gun I've most frequently carried over the past 8 years or so is a Kel-Tec P3AT, which has no safety. I carry it with a belt clip only, no holster, and I carry it chambered. It's not a safety concern to me, because it's a DAO pistol. the trigger pull is about 1" long and very heavy, and is small enough that my jeans act as an effective holster (keeping something from accidentally catching and pulling the trigger).
The most important things to consider are: 1) Keep your finger off the trigger until ready to fire and 2) Carry in such a way that nothing else can accidentally pull the trigger.
To do #2 effectively, you must know the firearm you carry inside and out. Know its safe modes of carry, and its unsafe modes of carry, and only carry it using safe modes of carry. Even beyond that, only carry in a manner you feel comfortable with - For some people, this means don't carry a 1911 cocked and locked, carry it un-chambered, even though C&L is considered a safe mode of carry for that firearm. For a DAO pistol, chambered and holstered is fine, and they usually don't have a safety. If that makes you nervous, don't chamber a round.
Finally, even though open carry is perfectly legal in many places, it's usually a good idea to conceal just to avoid freaking people out who aren't familiar with guns. I support the right to open carry, but I think a lot of people who do it are idiots looking for a fight, and that I don't like. If you do open carry and someone complains to you, be polite and encourage them to call police if they're concerned. Let the dispatcher be the one to tell them that what you're doing is perfectly legal and they should ignore you and move on with their lives. Don't be an ass about it, or you'll just give the rest of us a bad name.
*Side Note: "Autos" in this context means an auto-loading pistol, as opposed to something like a revolver. It does not, in this context, mean it lets off a string of shots every time I pull the trigger.