I have done 9 cruises and some are better than others for kids
Avoid Fred Olsen -nothing for children on their ships
Of the cruises I have taken 2 spring to mind
Royal Caribbean have lots of activities for children and are very family friendly
I have just come back from P&Os Ventura which is a lovely big ship aimed at families
It had a kids club with its own pool etc and from what I could see the kids were having a great time.
Royal Caribbean's Independence of the Seas (as well as Freedom and Liberty), P&O's Ventura and Princess ships; Crown, Ruby, Caribbean and Emerald all cater for children very well. Next bit is where do you want to go?!