I'm at a private school, but I'm going to chime in anyway. (Hope nobody faints.) One of our administrators was dismissed recently over a paddling issue. I knew that this man (who's a complete bonehead) had paddled a couple of students last year with the parent's permission, but this year he skipped that step. When the superintendent got wind of it, he wisely called the Dept. of Family & Children's Services and the police himself.
Paddling a teenager is ridiculous, in my opinion. As physical punishment, it's useless--the boys hit each other harder than a paddling every day in the hall. It may embarrass a student to the degree that he won't behave in a way that may warrant future paddlings, but it will probably just make him angry.
Paddling is way too variable. My father liked to remind me and my brother that he got his last spanking when he was 18 for whacking his brother with a cast. My parents spanked my brother when he was little because it worked. They stopped spanking me when I was about 18 months old because it just made all of us madder.
That said, "corporeal punishment" needs to be redefined.
However, I've found at school that physical consequences (which could be defined as "corporeal punishment") are rather effective with some students. For instance, my students know that if they are tardy, whether it is 2 seconds or 10 minutes, they have to do push ups. The first week of the semester it's 5 push ups, the 2nd week it's 10, etc. By the last week of the semester it's something like 105. I rarely have a student who is tardy more than twice, and almost none of them show up late at the end of the semester. It is a simple, physical reminder that there are inconvenient consequences for being late, and the principal behind having them do the push ups is similar to a smoker with a rubber band around the wrist.
I bounced my shoe off a student's head this year, but he deserved it.

(Yes, it was all in fun.)
This whole discussion, to me, misses the mark. I find more and more that I'm having to find ways to discipline students because they have no discipline in their lives. Parents don't teach them to be respectful, to act appropriately, to control their words and actions. My students learn quickly in my class that I don't have time to teach them basic courtesy, and if they don't learn quickly they are not allowed to waste my class time learning it. I don't use push ups for that--they either learn it from being sent out of the class to the principal's office or they learn it from peer pressure--by the end of the school year I could usually shoot a look at a student and have half the class telling him to stop acting like a jerk and shut up so we can go on. Much more effective to hear it from classmates than hearing it from the old lady at the front of the room.[/quote]
From teaching Sunday School, I can tell you it's the same. Sometimes the more affluent have the most unruly children, not learning courtesy and ignoring discipline. How many of us were 'seen and not heard' when the adults were visiting, etc. We had our own space to beat each other up.
Getting paddled when I was in school simply taught me ways to strategize my antics.

Fortunately, I went to schools with caring adults in control and abuse was not in the picture even for the most out of control students.
Discipline is necessary in schools, but I do not agree with paddling. Push ups sound pretty effective. ;-)