Your vehicle kit should contain items for both you and your vehicle. You need items to keep you safe and items for your vehicle (engine oil, tape, etc.). You can combine many of these items by using a hiking kit. Keep your hiking kit in your car to supplement your vehicle kit.
Bulbs for brake and tail lights
Bulb Grease in small package to apply to bulb contacts
Engine Oil: At least two quarts
Hose Clamps in a variety of sizes
Jack for tire changes
Jumper Cables to start your vehicle if the battery dies
Power Steering Fluid
Service Manual specific for your vehicle
Spare Tire and be sure it is inflated properly
Tire Pressure Gauge and make sure tires and spare are properly inflated
Tire Sidewall Repair Kit to temporarily patch larger holes in tires
Tow Cable or strap that can bear the weight of your vehicle
First Aid Kit that is well stocked and easy to access
Fire Extinguisher designed to extinguish A, B, and C fires
Air filter mask to help filter dust or smoke
Illumination: Flashlight and small lantern such as Streamlight Siege AA
Paracord can be used to make a shelter, splint, or emergency climbing rope
Plastic Sheeting (heavy plastic) to cover a broken window
Shovel in case your vehicle gets stuck in dirt or snow
Signals such as reflectors, flares, or flashing beacons to alert other motorists
(optional) Siphon to move fuel from tanks
Clothing, Shelter, Warmth
Hat with wide brim (waterproof)
Gloves that are warm and waterproof
Warm clothes including base layers
Rain Gear to protect you from bad weather
Reflective Vest to make you more visible on dark roads
Space Blankets: bivy, heavy 2-sided, lightweight
Saw to cut branches for fire, shelter, or clearing paths
Ax or Hatchet to cut wood or break glass in an emergency
Tool Kit with basics such as screwdrivers, pliers, ratchets, etc.
Food such as backpacking meals, energy bars, trail mix, ration bar, etc.
Water and Water Filter such as the Sawyer Mini or Sawyer Squeeze
Can Opener: Either a sturdy manual opener or an opener on a multi-tool
Backpack to carry supplies in case you need to leave your vehicle
Carabineers are useful for a variety of rescue purposes
Fire Starters such as storm matches, lighter, or sparker (have two fire starters)
Straps (heavy nylon) can bind your jumper cables, tow cable, etc. and have multiple uses
Tape (duct tape & electrical tape) for first aid, signaling, repairs, etc.
Zipties for repairs, shelters, etc.
USB Adapter to power devices such as phone
Device Cables such as USB to phone cable
Organize your vehicle kit so that individual items are easy to access. I purchased a double-sided parts box with clear plastic covers for less than $10 from Home Depot. I put the my first aid components in the parts box and added some vehicle related items. I can now easily carry all of those small items and access them quickly.
I organize the larger items using translucent ammo cans from Cabela’s. These are thick plastic utility boxes with watertight seal and heavy handle. I have one with car stuff including jumper cables, tow cables, flares, etc. I have a second with personal stuff including small tool kit, reflective vest, duct/electrical tape, rain gear, paracord, small lantern, etc. The supplies are organized and protected and I can easily transport them.