Should a person respect signs prohibiting guns in certain areas?

In some states, it is the law that one can carry a weapon into a business unless there is a sign posted. If a gun owner carries a gun into such a location knowingly, then they have committed a crime and are no longer justified in calling themselves a law-abiding citizen. In a location where this is not the legal standard then they have knowingly violated the property owner's right to self defense by violating their security of a gun free zone. What someone else may or may not do does not change that violation of someone else's concept of self defense on their property.

___As for businesses___
Prohibiting guns on their own private property I'd have to go with "Not a violation of your right to self defense." As a 'good guy' you have a choice to comply by their rules or take your business elsewhere. Obviously BG's will do as they please and the folks who frequent such places would be wise to take that in to consideration when analyzing risk.