I sometimes do, sometimes don't depending more on location, type of business/event and time of day. Your policy is a good one, esp. just not giving them your business, and I try to avoid them as well but I don't pay any attention to them if I have to go in.
I'm a Ky instructor and the most interesting discussions we have in class outside just the gun part is where you can and can't carry and how people respond to businesses posting the signs. It's not a crime to ignore the sign, all they can do is ask you to leave and if you refuse then it's trespass, but of course it's highly unlikely they'll ask since they won't know. It still leaves the question though of whether to observe it or not. Opinions vary wildly between people in the classes.
I'm no lawyer and I'm just speaking as me, not an instructor, but personally I liken it to the "no shoes, no shirt, no service" sign. You can walk in without a shirt on (and if you're Erin Andrews I even encourage it). That in and of itself isn't a crime. They can then either serve you and ignore their policy, which is fine, or they can ask you to leave. If you refuse to leave that's now a crime, trespass, and they can call the police. You can also choose whether to respect their policies and what they want in their business or you can ignore them and try to get by anyway.
Of course there are few such places in Kentucky. Not sure how I'd handle being under the rules some of our brethren on here endure who live in far less friendly confines.
Back to the OP -- As has been said it varies by state. I highly recommend a good class, esp on the law. Ky's is a 6 hour course with 2.5 hours of DVD video on the law. Dry as heck, but lots of important info on the responsibilities of carry. Definitely worth having.