Backpack or daypack;
Cash (at least $400.00 to $500.00), credit cards, list of passwords (preferably encoded, so that only you can read them) for your bank accounts, payment services, etc. You need that much cash to procure a hotel room for one or two nights, or until you get your bearings, if credit cards don’t work but hotels are still open;
Cell phone, charger, cable, external battery pack, solar battery charger;
Driver’s license, car registration card, passport, Social Security card, Medicare card, auto insurance ID cards, etc. (in a waterproof plastic bag);
Fire extinguisher, flares, waterproof matches, Bic® lighter, ferrocerium rod fire starter;
Freeze-dried, canned, and preserved foods (beef jerky, pemmican, trail mix, granola, etc.), MREs (Meals Ready to Eat–most MREs don't require any heat to prepare or have chemical heating systems);
Gloves – to protect your hands if you need to cut firewood or if you need to repair your vehicle;
GPS Receiver/Navigator, ham radio, shortwave radio, walkie-talkies, CB/GMRS radio, satellite phone, compass with maps of your areas of interest;
Mess kit – frying pan, pot, coffee pot, Sierra cup, eating utensils (spork), etc. – you may want to use disposable paper plates so that you don't have to use precious water to wash your dishes;
Pepper spray or taser, other self-defense items;
Personal mobility and healthcare items – stroller, cane, walking stick, blood glucose meter, etc.;
Pet equipment – grab your pet and any pet food that you need. Don’t forget the pet’s water bowl, food bowl, dog/cat bed, etc. (It’s probably best to leave your aquarium behind, if you have one.);
Poncho, rain jacket, down jacket, tarp;
Prescription medications you need, along with any recent prescriptions that your doctor may have written for you. Toilet paper, sterile alcohol wipes, sanitary items, soap, hand sanitizer, etc. – be sure to have some polarized sunglasses and a spare pair of prescription eyeglasses, if you need them, and a recent optometrist's prescription;

Vehicle BOB – this bag should already be in your vehicle, ready to go – see the Vehicle BOB items list below.

Emergency sleeping bag (“Bivy sack”) or wool blanket;
Canteen, Grayl® 24-ounce Water Purifier Bottle, Stanley® thermos;
Duct tape (or Gorilla® tape);
Extra warm clothing, poncho, 550 paracord or #36 Bank Twine;
First aid kit, tourniquet, BleedStop® (stops the bleeding of everything from minor cuts to large bleeding wounds);
Flashlight or headlamp (ideally, both), a lantern (with a setting that sends out a “SOS” light pattern), candles, kerosene lantern, solar panels/solar generator (don’t forget the cables for this);
Hiking boots (you may have to walk for miles if your car breaks down and/or if there is an EMP attack);
Knife and multitool, knife sharpener;
Mess kit – frying pan, pot, coffee pot, Sierra cup, eating utensils (spork), etc.
Shovel – collapsible; axe;
Snacks – such as beef jerky, pemmican, granola, trail mix, protein bars, etc.;
Spare batteries; GPS navigator (don’t need this if your vehicle or smartphone has one), compass with local map;
Stove – collapsible backpacking stove, such as the Gas One® backpacking stove or a simple, small woodburning or alcohol stove; waterproof matches; Bic® lighter; ferrocerium rod fire starter;
Water filters, such as Grayl®, Katadyn®, LifeStraw®, Sawyer®, etc.

PDF file of the above lists

Here's an excellent BOB list on the Trueprepper.com website.