You will want to pick the cruise lines with the best kids programs. They seem to be able to keep the kids occupied and when you do see them it is usually on Lido taking in the fun at the pool.
You will also want to go when there is no school holidays. Xmas, New Year, spring break, summer, and stat holidays are good times to avoid. I was on the Valor in January 4-11 and I didn't realize that many schools in the states didn't go back until the week after schools go back where I live. There were many, many, many kids and some of them not so well behaved.
You'll want to stick with Carnival, RCI, Norwegian, and perhaps Celebrity. I do encourage you to check out what they say about their kids programs because it will tell you if they are able to manage and keep the under 12's occupied most of the time so YOU have a relaxing time without crying/bratty/cranky kids around!!! Otherwise, you will never be able to avoid kids on a cruise because parents with kids under 6 can take them at anytime....
2007 Victory & Triumph
2008 Conquest & Liberty
2009 Valor, Freedom, and Splendor
2010 Glory and Liberty
The longer the cruise, the fewer children there will be on board. Its just the way that it works out. So if you take an 8+ day cruise, there will be some kids but not a ton.
Life is too short to let the ship of your dreams sail without you.
Carnival Destiny Feb. 2006
Carnival Fascination Feb. 2007
Royal Caribbean Grandeur of the Seas Feb. 2008 The DTW & MsBJ tour
Carnival Valor MsBJ and Dina Feb. 2009
Carnival Glory MsBJ and Dina Feb. 2010
Carnival Dream MsBJ and Dina Feb. 2011
From past experience, go on Celebrity if you want to be "kid free." Have taken 4 Celebrity cruises and have seen few, if any, children onboard. A friend told me that Holland America is also another cruise line that does not cater to kids. A friend went on the Celebrity Solstice this past January and said the average of the passengers was well past 70, so be aware that this cruiseline is much more sedate than others.
I cruised with Costa and found the kids were not a problem, they had great programs and I think even private nanny's. You might see them at the main pool during the day. I usually go to the Aft pool it's adults only, however it's not always enforced. I am cruising in September so the kids are back in school, I've heard Christmas cruises and Spring break one's can be a nightmare. I think that HAL,Cunard,Celebrity,Crystal, would be good choices if you don't mind that most of the cruisers are going to be seniors. Other wise it's a gamble. I think most cruisers with kids choose Disney, Carnival for price, or RCL for variety of things to do. True longer cruises will have less also.