Yes. There are an abundance of cruise lines who have ships that cater particularly to families with children of all ages. P & O's Ventura, Royal Caribbean's Independence of the Seas seem to be hot favourites at the moment for those who seek a cruise with lots to do, plenty children's (and adult!) facilities and not too 'stuffy'.
Best places (most popular) are the Caribbean (Oct-April) and the Med (April-Oct). Make sure you do your research (read the reviews - check out P & O, Royal Caribbean, NCL and Princess), talk to cruise specialists (not your average travel agent on the high street) and check out cruise line's websites to give you more accurate and up to date information on their ships and places they visit. Generally speaking the more passengers they cater for (2000+), the more facilities they have, especially for kids. Hope this helps.
I have cruised since I was 5 years old and my children now 12 and 18 have also cruised all their lives. Children are so well catered for if you choose the right family orientated ships. There are at just the right age at the moment 4 and 8 to enjoy all that a cruise holiday has to offer.
Took my grandaughters aged 4 and 7 on their first cruise last April on a RCI ship. They LOVED it. The 7 year old even offered to pay for her own babysitting fees for after 10pm because she loved the childrens club so much, at home she is the sleepy one and is in bed by 7, and the 4 year old asked for another cruise(caribbean) for her 5th birthday. I can only speak for RCI and Costa about the childrens clubs, but both lines made the childrens days, and I knew the children were safe and well looked after. A cruise is for all ages. So much to do each day.
Absolutley ... independence of the seas or a voyager class ships with royal caribbean ...