I tell people that on the ship, Mom is on vacation too. At WDW, Mom still is "on duty" making sure that everyone gets to do at least part of what they want to...everyone gets a chance to eat where they want...no one is "starving," etc. On the ship, if you are hungry, you just don't get it--there is always something open where you can get food. If you can't find something to do, you're not making ANY effort at all. And the wonderful thing is that you don't have to stay together as a group.
The ship is really a very safe place. DD had the run of the Magic at a far earlier age than I would let her go on her own in a park (I barely do that now...and that's at 17 with a friend and a cell phone!) Of course, you each know your own kids and whether they are mature enough to be off on their own. Also, for parents of teens...we've noticed that the personality of the teen group can vary from one cruise to another. We've had some where there was a really nice group of kids and others where there was somewhat of a "mob mentality" with kids getting older sibs to buy them alcohol, etc.
We have several firm rules--DD is not allowed in anyone's cabin and no one may come into our cabin. The drinking age on the ships is 21--nuff said on that. And if anyone is bothering you, find the nearest CM (and they are always near!) I'm not trying to scare any parents of teens--you just need to be realistic. I guess we've always been a lot more strict than many families.