Well as a mother of four kids I am firmly in the no camp but there are others who are firmly in the yes camp.
I think that there are arguments for both sides on this and the main one is the behavior of the children at hand.
My children are no angels and they are warned when we go away that they are to treat their elders with respect and to not cause issues with other passengers, however there are times when some of the other passengers should also be responsible for their behavior.
On our cruise last year I was disgusted to see adults pushing in front of my two youngest in the buffet queue and this only stopped when I joined them. Similarly when they were in the family pool they were almost drowned by one gentleman who was swimming laps as he thought it was his right to be the only one in the pool even though my children were also doing laps. The final straw for me was when we were in a lift and my son was asking people as they entered what floor they wanted as he was near the buttons and a lady slapped his hand saying he was messing with the buttons. How I stopped myself from slapping her hand I do not know!!
If you do not want children on a ship then choose a ship that is adults only, there are plenty out there that will cater for you.
On the other hand I have seen children in lifts racing up and down in them, diving in the pools and splashing other passengers and racing around the decks like bats out of hell. This kind of behavior is not acceptable. When I worked on the ships I was often asked to intercede but is it really the crews responsibility to do this because if there is subsequently a complaint then you can lose your job! Surely the parents of the children have to be accountable.
I for one love taking my children on a cruise and enjoy spending time with them but other parents seem to feel that once on board they do not have to accept parental responsibility.
Would be interesting to hear your views on this and if you have ever had a cruise ruined by unruly children or other passengers or both?