Depends on if you are wanting an "on sight" kit or a "grab and go" kit OR things to have when you go hiking/backpacking.
Hiking --
a couple of matches and some fire starter. They don't have to be waterproof (or you can do it yourself by dipping them in wax), but need to be in a waterproof container. Firestarter can include a bit of paper, dryer lint,-- just about anything.
a whistle WATER &/or a small water filter (both, really) & container
stocking cap sweater, jacket, etc --enough to take you through a night for light weight "bang for the buck" -- a pair of nylons is good insulation and very light weight.
a MAP a snack -- preferably something you don't particularly like so you won't eat it unless it IS an emergencyBACKPACKING You should have most of what you need, just keep the above with you for "day trips". Also, try to have 1-2 days food and water left over. And, even if you know the area very well, a Topo map is a good idea in case you find you don't know the area so well.
"GRAB AND GO" Water,
preferably enough for 3 days (include washing and cooking!) You can buy it or "make your own" by putting it in clean bottles with a couple drops of chlorine and sealed/tapes. Figure a gallon a person.
soap and/or handwipes You DON'T want to get sick!
medications, plus a valid perscription. ***
you should have a week or two's worth of anything critical since you won't necessarily be able to get a refill right away, particularly if you have to go out of state. Food for 2-3 days You want things your family will eat, best NOT to get unusual stuff, expecially if you have kids. (this is the time for the can of their favorite) Cans are heavy, but usually can be eaten cold if needed. I keep dried jerky, jello with fruit and fruit cups, eradiated milk and cereal. -- but go with your family's likes.
Diapers, change of clothes for little ones any cloth can work for diapers and you can "wash/rinse" them in non-potable water (not too nasty).
Blankets/sleeping bags Bare minimum is jackets, space blankets and a tarp. (to stay warm in your car or possibly in the open) A tent is nice, but bulky and expensive if you don't backpack.
Nice, but not absolutely critical: a Change of clothing (or at least underwear) -- but note, a change or two is a necessity for little ones. Toys/coloring books/cards Think simple, lightweight and a lot of different uses.
PETSDon't forget pets! Sure, your life does come first, but plan ahead so you have options. A bag of food and a carrier of some type (even one "jimmy-rigged" from cloth, etc at the last minute) can make them "transportable" at least to a shelter in a safer area.
STAY PUT basically plan on staying put a minimum of a week, probably 2 without services being fully up and running. Include gas, fuel for stoves, emergency power source, radio, etc.
WATER: Now is the time to fill jugs of water and seal. They should last for a few months just like that. If they get cloudy, the water can be drunk if boiled or sterilized with bleach. (or just used for other things). When you get warning of an emergency, fill your tub and basically any container you havet hat doesn't leak with water (pots, pans.. but even garbage cans). Think not just drinking, but washing.
Toilets -- if the sewage system is working at all you can flush with old wash water, even polluted water (just be careful not to touch it). If not (particularly in floods), use a
bucket with charchoal and some plastic bags. The bag is the liner (2-3 is even better), lay charcoal over the waste, use again, make another layer.. until filled. Be careful not to let the smells build up, though, they can make you sick over time. (if you cannot deal with sanitation, its time to leave).
Bleach -- for sterilizing drinking water, cleaning, disinfecting. Most people have this, just think of keeping an extra gallon or two on hand (or buying when an emergency is pending). Iodine tablets work for water, but are expensive and more perishable.
Flashlights and/or lanterns and batteries to run them.. OR get one of those new "crank" or solar powered ones.
Radio-- particularly with the weather channel on it. Again, they have nice ones that can run by battery, hand crank and/or solar power.
First aid kit -- you should have one anyway, but think beyond just bandaids. The key here is to also know how to use it. Doesn't do much good to have splints if you don't really know how to use them!
Medicines*** don't let anything critical get below a 2 week supply.
Food -- Think cooking without utilities. Solar ovens, sterno cans, camping stoves, etc. Few things boost the spirit like decent hot food. You can get fancy kits of either "ready to eat" or "just add water" foods, but in most cases you are better off just sticking with the types of things you eat every day, perhaps somewhat simplified. Even a few "regular" items can make a big difference in how people feel.
Games/books, etc. -- don't forget the entertainment. A deck of cards goes a long way, but think of things your family enjoys normally. Its good to have a "secret stash" of special toys and such to entertain kids in an emergency. They don't have to be fancy, just something that they will enjoy that is different. from their regular toys. (a new Lego, a new coloring book... etc.).