A family vacation can be a hassle free trip provided you have all the gear you need. To avoid leaving behind things that are really important, begin creating a checklist a couple of weeks before your flight, and add things to them over the days. If you sit down to make a list a couple of days before the trip, you're likely to forget something that strikes you later - when you're on the plane!
If you have a baby, your bag should contain the following items:
Travel Stroller
Lots of diapers
A changing pad
Diaper rash cream
Stroller
Front pack or backpack
Feeding bottles
A feeding bowl with lid and spoon
Sterilizer
Bibs - lots of them
Baby wipes
Pacifiers
Baby toys
Tins of formula
Bottled water
If you have a toddler, don't forget to take along:
Lots of clothes if you don't intend to do laundry. If you want to take a limited number of clothes and do a few wash cycles during your trip, leave behind jeans and other clothes that take forever to dry. Light fabrics that dry in a few hours are ideal. For boys, pants that can be unzipped to create shorts are good for separate looks with the same clothes. Take along two or three sets of swimwear if you're heading to a warm climate, and lots of jackets and vests for colder climes.
If you have a stash of old clothes that you want to get rid of, take them along on your trip, and throw them after they've been worn a couple of times. It'll cut down your luggage dramatically.
General
No matter how many of you are on the trip and how many kids are going along, you'll absolutely need
A first aid box with essential medication, bandages, gauze, anti allergen medication and other must haves
Trash bags for wet clothes.
Camera
Zip lock bags to store little things like your daughter's accessories and hair pins.
As far as possible, try to compartmentalize your possessions into separate zip lock bags. It makes finding everything in a hurry a lot easier if you just have to glance at a few bags, see their content and find what it is you're looking for instead of rummaging through clothes and more clothes to find a safety pin.