Ask about children's amenities. Check in advance with the cruise line to make sure the ship you're sailing offers things your child might need. Are cribs available? Children's menus?
Pack some basic first-aid supplies plus any medications your doctor may suggest, and even a thermometer. Cruise lines have limited supplies of these items (and charge for them, too) and can quickly run out if the ship has many families aboard. If an accident should happen aboard, virtually every ship afloat has its own infirmary staffed by doctors and/or nurses. Keep in mind, first aid can usually be summoned more readily aboard ship than in port.
Warn younger children about the danger of falling overboard and make sure they know not to play on the railings.
When in port, prearrange a meeting spot. If your child is old enough to go off on his or her own, prearrange a meeting spot either on board or on land, and meet there well before the ship is scheduled to depart to make sure no one is still ashore.
Make sure your kids know their cabin number and what deck it's on. The endless corridors and doors on the megas look exactly alike.
Prepare kids for TV letdown. If your kids are TV addicts, you might want to make sure your cabin will have a TV and VCR. And even if it does, they should be prepared for a little bit of withdrawal, since televisions on ships just don't have 200 channels of cable--you'll be lucky to get five or eight channels. On the bright side, big ships are likely to have nightly movies and a video arcade.