My suggestion would be Royal Caribbean as a top choice (but preferably not when I'm on) ....Other brands are also available......Nei.
RCI are generally considered to have the best activities for children - rock climbing wall, iceskating rink etc, but the newer NCL ships are introducing Wii.
Royal Caribbean - we have been with kids now 6 and 8 three times in Caribbean and Europe and are going again twice this year. Truly a holiday for everyone - especially mum! If you can, get interconnecting cabins (cheaper in the Caribbean) but sharing a cabin didn't prove too tricky around the med because there is so little time spent in the cabin. The drop down beds were considered fun. Our kids would go on a 'no port' cruise if they had the option! That has to be an endorsement! Choose one of the bigger ships - at least one with a dedicated kiddie pool - skating rink optional as far as we are concerned. Activities in the kids club are fantastic and the folder of 'work' they presented us with at the end of the 12 med cruise would put a lot of schools to shame!