If you definately don't want ANY kids around, then I would suggest Crystal cruises or one of the more upscale cruiselines. Any of the mass market (Disney included) will have a handful or more of children.
What it comes down to is this then:
Itinerary Where would you like to cruise to?
Departure Port Where do want to sail from? Figure in costs of airfare etc.
Size of ship Yes, it does matter!

Do you want to cruise with 3000, or 30? Think lines, show seating etc.
Finally, just to add my .02 cents in on different lines: We have sailed most of the mass market cruise lines so I can compare for you:
Princess: classy, more formal, restricted # of kids per sailing, great service, average food, decent shows. LOVE personal choice dining.
RCCL: great service, TONS of kids...constantly under foot, LOTS to do...not relaxing at all, pretty decent food, other than ice show...hated shows, smokers everywhere!
Carnival: YUK! nuf said.
Disney: great service, passable food, nice rooms, love the shows (yes, even after three times!), don't notice kids too much except at pools, and in elevators, love the rotation dining.
That said, if you like WDW, I agree with the others, you will like
DCL. They do a far superior job at keeping the adult only areas...just that! NOW, if they would only enforce the ADULT ONLY issue and the Adult entertainment series!!
HTH
Lisa