I was on Carnival Breeze for a Thanksgiving cruise and all of the kids seemed to be having a ball - and there were hundreds of them.
Yes, sometimes they would leave the organized activities and you would packs of them "roaming" the ship, but I noticed one thing - that all them had been well instructed about their manners even when they are on their own. I suspect the youth counselors did this, because not all parent would think of it.
As these kids roamed the ship, yes they would run and cut in front of you. (kids will be kids) but I also noticed that they were always fairly quiet, and if one them yelled out, the others would immediately "shush" them - reminding each other not to yell out in public areas.
All in all, they were pretty well behaved, even out on the pool decks and in the play area.