This time of year, we go through last year's kits, take out the medicines, food items, paper supplies, batteries, etc., and replace it with new ones from the dollar stores. Pretty much the usual stuff, but here's what we learned we needed when we had to live in a tent with no power after Hurricane Ike:
A Ziploc bag containing copies of essential documents (drivers licenses, insurance cards, birth certificate, etc...) just in case you do have to evacuate
First aid kit with everybody's medicine (allergy stuff, Rx stuff, Advil and aspirin, saline solution), bandaids and Bactine, small bottle of peroxide, Pepto Bismol tablets, etc. Personal care items like razors, soap, hand sanitizer, bug spray, toilet paper, feminine hygiene products, tooth paste and tooth brush, all fit into a zip-lock bag easily, and are cheap at the dollar store.
Battery operated fans and lights that bright enough to read by at night
Socks. Lots of dry and clean socks and old, clean tennis shoes.
Kitchen matches, lighters, firestarter cubes, charcoal briquets, newspaper, grill (have these all together where you can get to them)
Old metal skillet that will get messed up using it on the grill. A couple of sharp knives - a paring knife and a chef's knife is good, along with a bunch of silverware, pancake turners, pizza pans, a hand can opener, serving spoons, etc. A whole box of plastic tableware, paper plates, napkins, paper towels, stuffed in the garage is a good idea.
A couple of decks of cards, travel size games like Connect Four and Jenga, connect-the-dots and word search puzzles, anything that you can do without electricity or the internet is handy as hell to have on hand. We played a LOT of cards at night, the first few days after Ike.
Wind-up radios came in very handy, but the wind-up kind of flashlights were a pain in the neck. I keep the radios in our kit, along with a ton of dollar store batteries, but for flashlights, we use two of those big, cheap yellow flashlights that float, like these (Home Depot floating lantern)
A box of dry, clean clothing, old towels and sheets, extra shoes and socks, an umbrella, a couple of blankets, and some pillows. Great place to keep old beach towels that have snags or just towels you don't use anymore.
Shoes when you're wading through water. Though you want them cheap enough that you won't feel bad about tossing them if you have to wade through contaminated flood water. As an accompaniment to that - clothing that dries quickly.
Ziplock bags and trash bags to keep things dry.
Sanitizers: Hand sanitizer, clorox wipes, body wipes
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