What kind of gear should you keep in your vehicle?

Ask yourself what you are preparing for. It's really unlikely you're going to be shooting your way home.

Vehicle breakdown or an impassable road (snow or ice storm, fallen tree or other part of the landscape, crashed vehicles) are by far the most likely scenarios, so you need to be prepared to be stuck with your vehicle for an extended period. It would also be prudent to have the supplies needed to abandon your vehicle and head for home if absolutely necessary, but in the vast majority of rescue scenarios it makes the most sense to STAY WITH YOUR VEHICLE so that you can be found more easily. A great many prolonged search and rescue operations involve trying to find some badly dehydrated or dead soul who wandered off into the wilderness after they were reported missing and their abandoned vehicle is quickly located. A car is MUCH easier to find from the air than a person, particularly in wooded areas where foliage blocks much of the view from overhead.

Environmental exposure is going to be your greatest threat to life most of the time, either extreme heat or extreme cold. You need layers of clothing. A base layer of merino wool or synthetic blend depending on your budget, insulating midlayer, waterproof outer layer, extra socks, boots, hat, face covering, gloves and mittens (mittens are warmer than gloves but lack dexterity, so have both to fit different situations). Layers are equally useful for extreme heat, shielding you from the sun while trapping moisture.

Wool blankets are really good because they're inexpensive, and will still insulate you even if they are wet (contrasted with down, which is extremely warm when dry but loses all insulating abilities when wet), but they are bulky. A decent alternative is reflective emergency blankets: they're cheap and light, they reflect heat back to you, or can shield you from the sun. You can buy the cheap Mylar reflective blankets for a dollar or so apiece, or spring for the plastic-backed ones with greater durability (made by SOL) for a few dollars more. The cheap ones rip very easily, and you can pretty much forget about being able to fold them back down as small as it was in the package. SOL makes a few different ones, including a reflective tarp, but apparently the tarps have an unpleasant off-gassing odor.

A tarp would be good for an impromptu lean-to shelter, or if you need to crawl around on the ground to repair your vehicle.

WATER is essential to survival. You should have plenty of water in your vehicle, the general rule being a gallon per person per day. Some means of water procurement and purification are also excellent to have. A 4-way Sillcock Key is good to have for water procurement in urban areas from the outside faucets of commercial buildings in many areas.

FOOD (Non-perishable) is also necessary. If you include canned foods, don't forget a can opener. Shelf life of most foods will be greatly decreased in the high-and-low temperature swings of a car's trunk. Same problem with water. Plan on replacing consumables at regular intervals.

Toilet paper and disinfectant wipes for hygiene. A pack of baby wipes will probably dry out, but you can add water at any time to restore them.

A basic medical kit, more advanced depending on your level of training

A light source. A headlamp is great to keep your hands free. Extra batteries. Check and replace them regularly or they'll be dead and leaking when you need the light.

A spool of paracord is endlessly useful.

A hi-viz vest and hazard markers like triangles and road flares to reduce the chance of someone running into you or your stopped vehicle. These aren't fool-proof, though, and people get killed on the side of the road all the time by careless drivers. That's why emergency vehicles even with flashing strobes park in a "standoff" position (parked at an angle with their wheel turned) so that if another vehicle hits them, they'll veer off to the side instead of being pushed into emergency personnel or the disabled vehicle. If at all possible, get your vehicle the hell away from the traffic lanes.

You need to be able to get your car moving again if possible. You need basic tools for changing a flat tire and doing simple vehicle repairs (hoses, hose clamps, fuses, wrenches, pliers, things like that). Make sure you have a jack, lug wrench, and a spare tire, and check it periodically to ensure it's actually still inflated. Jumper cables. Optionally, a booster pack to jump-start the battery, but you need to make sure it stays charged.

You also need a decent shovel for digging out obstructions. A short-handled flat metal transfer shovel with a D-handle works pretty well for snow and won't snap like plastic ones can. A metal shovel can also dig in the dirt whereas a plastic snow shovel cannot.

Something to give your tires grip such as traction pads.

Snow-melting salt.

An off-road vehicle should have a winch and recovery straps, but most vehicles can't take full advantage of this. A hand-cranked come-along winch might make sense depending on your vehicle.

A folding pruning saw or a hatchet may be useful for removing tree limbs, but expecting to cut up a huge tree that's blocking your path isn't realistic.

Communication device. You probably carry a cellphone. A means of charging it like a lighter socket adapter and charger cord, and a power bank.

A little cash. If you're in civilization, this could be your most useful tool for getting home.