Spices. People always forget spices. Sure, you can survive without seasoning but your food may be bland and tasteless.
Don't forget general use medications like aspirin. Lip balm might also be good. Lotions too. Just because it's the apocalypse doesn't mean you need to have dry, flaky elbows. Mouthwash and toothpaste. Or, in lieu of toothpaste, stock baking soda which can be used as toothpaste plus other uses. Also, a toothbrush. Preferably more than one. Antacid. Potassium iodide tablets, just in case. Shampoo and soap.
A sewing kit. Scissors.
Copies of important papers.
Bleach, vinegar, rubbing alcohol and witch hazel are also good to have on hand. Also, baby powder, borax, calamine lotion, epsom salt, hydrogen peroxide and vaseline.
Try to get tools that serve multiple purposes too. As an example, I have long carried in my pocket a manual can opener that also works as a flat-head screwdriver. Multipurpose tools can be great space savers, but you also want functional tools so you need to be careful. Just because something has all the bells and whistles doesn't mean it's going to be practical. I have a pocket tool that has a screwdriver which is good for occasional use, but it's not as easy or fast to use as a normal screwdriver. So for tools you know or suspect you may be using a lot, you'll probably be better off with the actual tool rather than a multi-tool in those cases. Locks might also be handy especially for situations where you might need to be more mobile and will need to secure things overnight or if away. Likewise, have bags on hand in case you need to be mobile. A backpack. Ziploc bags and garbage bags too. A 5-gallon bucket or two or three which can double as storage (get removable lids).
Don't forget food, medicines and treats for pets. A leash can be handy too.
Don't forget cleaners and wipes for glasses or any medical devices you require.
Baby blankets (even if you don't have a baby) and regular blankets are good to have as well as an emergency blanket. Also a tarp. Strong rope. Compass, mirror, whistle. Tweezers, nail clippers, nail file. Duct tape. A folding shovel, hand-held chain saw and an axe. A hack saw. Hammer, screwdrivers, wrenches, pliers. Glass breaking tool. Clips, rubber bands, string. Tape measure.
Towels.
A lighter. Water-proof matches.
Toys for kids. Sporting goods for all ages. Playing cards and board games. A small chalkboard for Tic Tac Toe or other games. Dice. Chalk, crayons, paper.
A permanent marker. Wax marker. Pencils, pens.
Perfumes and colognes. Mints and breath spray. Just because it's the apocalypse doesn't mean you won't meet someone.
Others have covered food, but be sure you also have utensils. Toothpicks might also be a good idea. Cooking gear. A collapsible cup. Plates or eating tray. A portable sink. Dish soap. Sponge.
A solar charger is good as are rechargeable batteries. Might be useful to consider other power alternatives as well, such as batteries that run on salt water.
Self-defense items, like guns (and ammo) or knives. A big stick which can also double as a walking stick or cane.
Also, something to serve as money. In some situations, cash will do. In others, you may want silver and gold coins, ammo, extra tools and goods for trade, leather goods, cigarettes, etc.
Okay. I give. Why toilet paper?