As a not, some stuff might be a repeat of what I listed here, but some of that was specific to the situation of having electricity and running water. This is more "worst case scenario" based.
Kits I've created for my family and me include but aren't limited to the following:
Food and Cooking
Several gallons of water for each person (enough to last several weeks and includes both consumption and regulated bathing -- I've been here a year, and things don't seem to last longer than few weeks)
Water bottles and bottles of water (for carrying purposes and refill-ability, though gallon jugs are also both but not everyone wants to carry jugs around constantly)
Water purification tablets
Portable water purifying systems
Enough dried food and canned food to last each person several weeks (some examples I have are peanut butter, dried fruit, canned juices, nuts, beef jerky, granola bars, energy bars, variety of canned foods like the spaghetti and meatballs in a can)
Manual can opener
Portable pots and pans
Reusable plates and eating utensils
Dual burner cooking stove with fuel (such as propane)
Gear and Tools
Flashlights and camping lanterns (a head lamp is useful in these situations)
Batteries, rechargeable batteries
Solar chargers (I found chargers that recharge with solar energy)
Candles
Matches, water-proof matches, a fire-starting kit that includes flint and a striker
Flares and glow sticks
Blankets and sleeping bags
Tents
Walkie talkies
Hand crank radios (though I don't know that anyone uses the radio here for emergency broadcasts)
Whistles
Masks (the kind for dust and ash and debris, N95 is preferable)
Multi-Tool
Duct tape
Rope or paracord
Plastic sheeting
Garbage bags and ties
Something called a Luggable Loo with biodegradable bags and biodegradable cat litter (yes it is what it sounds like)
Weapons (such as a crossbow, gun, knife -- rifleman's hawk is good and versatile)
Sewing kits
First aid kits (I want to say this is likely self-explanatory and may vary depending on your personal needs and level of comfort but mine include things like bandages of varying sizes, needle and thread, alcohol wipes, rolls of gauze of varying sizes, antibiotic ointment, a few pairs of gloves, tweezers, forceps, scissors, antibacterial wipes)
Personal Items
Toiletries (such as toothbrush, hairbrush, moist towelettes, toilet paper, hand sanitizer, soap, feminine hygiene products, hand towels)
Several changes of clothes (including socks and underwear)
Jackets
Rain ponchos
Activities (coloring books, reading books, board games, playing cards, as examples)
This doesn't include water/weather resistant bags for fast travel if needed, though if we're stuck on an island there's a greater chance of sustained, permanent shelter. And, of course, I try to cater to each person’s individual dietary restrictions and medical concerns. (For instance, I need a lot more calories than the average person. My food supplies are made with that in mind.)