As Brian says, go with the right company and there will be no problems.
Problem with Carnival, Celebrity and Royal Caribbean is that they do tend to cater for young families, the majority of whom are excellent in their behavior.
But they also tend to attract some of the 'rat bag' brigade.
Worse one here in Oz is P#O as they want to attract mainly the 18 to 25 age group who will spend most of the day at the bar. Good profit there.
We have done 18 cruises and only on one was there any problems. Couple of fights between just two who were put off at the next port
Princess do tend to attract the over 45 brigade and a few families.
Security is good and when you see some of the guys they employ you can see why, very friendly but do not get on the wrong side of them