For the most part, kids who scream, act out, misbehave or generally raise a ruckus in public are poorly parented. Exceptions aside, it's typically an issue of the parent not disciplining the behavior early enough, and turning a blind eye to it the more it happens. I can't stand those unruly kids, either, but they're not going to go away, ever.
I figured we would all have a similar point of view here.. but it's an interesting topic.
I personally cannot stand loud disruptful children at a restaurant that I am paying decent money to eat at. I fully support this restaurants sign. It is the restaurants perogitive to do what they need to do to preserve the environment that they are trying to create for their customers. My girlfriend often says that I overreact about this situation (though I never act out or say anything to anyone, I just get annoyed). Many parents are under the belief that they have the same right to eat there as anyone else and people should respect that. It is something that I disagree with for a multitude of reasons, the most of which being I'm not in your earhole throughout your meal and I'm not sprinting around your table playing tag. Please, If you can't get your children to act in a respectful mannor, order your food to-go and have a picnic in the park. Thank you.
I don't have a problem with disruptive kids in a restaurant, mainly because I've never really faced that problem. I tend to patronize restaurants that are aimed more at singles and couples, not a more "family-friendly" restaurant like a chain restaurant or a local upscale family-oriented eatery. I'm usually not mindful of that when picking a restaurant but those tend to be the places I frequent for really good food and/or excellent booze. The closest I've come to sitting in a noisy environment is the dim sum places but I don't mind the ruckus really. Personally, I would be much more peeved about people bringing their dogs to a restaurant or any public place (other than a park) than I would be about bratty kids.
What's worse than unruly kids in a restaurant is unruly kids on a flight.
People don't have some kind of right to only hear sounds that they find pleasurable as they go about their day. If you don't want to be subject to crying babies, screaming kids, or whatever other sounds you find annoying, stay home. That or suck it up and deal with it.
That said, parents need to step their game up. If a toddler or young kid is throwing a screaming fit in a restaurant, store, park, plane, train, or automobile, it's probably because his parents are lames. It's not that hard to have kids that aren't out of control. Now, if an infant baby is crying, that's a little different and far more difficult to control, but one could certainly step outside with the baby until they could soothe it. Parents need to be more considerate of others when their baby is being disruptive, others need to grow up.