I'm a bit shocked by some of the responses here. God! The lack of compassion or understanding is mind boggling. Yes, there are bratty kids everywhere whose parents are too permissive and the child's behavior suffers as a result.
But there are also children who are on the autism spectrum, or have mental or sensory or emotional challenges who sometimes become overwhelmed or over stimulated in social environments. Does that mean the child should be confined to their home, or their room, and never taken anywhere so as not to disturb anyone? The parents of those kids make difficult choices every day revolving around how much stimulus is good for their child this day, what is in the best interests of the kid right now, will this or that choice work for them, what will the day be like if I do choice A or choice B for my child...and on and on.
Corporal punishment will not solve that.
Separate from autism or other mental challenges, emotionally healthy children experience every single emotion that you as an adult feel, whether it's love or rage or frustration or happiness...every possible emotion on the spectrum, but their young, inexperienced selves have no clue how to process some of the bigger and more overwhelming emotions. It's the parent's job to help the child deal with those, not by smacking the emotion out of them, or telling them to shut up, or not taking them anywhere, but to HELP them deal! To educate them in how to process what they're feeling. And yes, certainly, remove them from the environment if they become too upset, but dammit don't remove them because they're disturbing others, as a punishment for their "behavior" like they they're doing it on purpose! They can't effing process what's happening to them, what they're feeling!! Take them away to somewhere quieter to help them deal with what they're feeling!!!
It frankly enrages me to see or hear folks who think these kids are just willful, or screaming for attention, or being "bad" ....whatever the !@#$ that means! Sure, there are kids who just blatantly misbehave. No argument. But for every one who does, there are several more who are struggling to manage the emotions that they're feeling that are too damn big for them, that they don't know what to do with or how to express or how to manage. They need tools and education, not a swift smack or your anger.
If you as an adult with your range of emotions were treated the way you're suggesting the child be treated, how would that make you feel? I'm not taking about when you were a kid and you WERE treated that way. I'm talking about now. I don't think you'd take it very well. The child who is acting out in the supermarket is feeling all the feelings YOU feel as an adult, but is woefully unprepared to deal with them.
If you want to get angry, get angry at the parent who hasn't taken the time to educate him/herself as to the best way to deal with the upset child, and so is either ignoring the kid completely because he/she doesn't know what to do, OR is just trying to shut the kid up because he/she knows people around them are going to get angry at the noise. Either response is going to make matters worse, and perpetuate the situation. Well, unless the intention is just to make a good little robot of the kid, break him. Then yeah, go ahead.
Sheesh!