Great responses in this thread so far, I'll add some less glamourous absolute must-have items that I recommend for anybody going into the wilderness, especially if you typically go as a solo vehicle.
1) Maps - Have a map of the area you are exploring. Spend some time getting generally familiar with the area before you head out. Consider alternative routes as backup options in case you encounter a locked gate or impassible obstacle. If you are using only electronic maps, make sure you have a way to recharge the device, without requiring the vehicle's power if possible. Paper maps and compass are the best backup. Share a photo of your rig, including make/model and share at least generally where you are going and what your general plan/timing is.
2) Flashlights - "one is none, two is one" - I recommend at least three source of light, bonus points if you also bring extra batteries or other way to recharge them that does not require using your vehicle.
3) Recovery plan and equipment - if you get stuck, how will you recover yourself? You'll need some sort of recovery gear, this could be a shovel, it could be a winch and a bunch of rigging. it's a huge spectrum, know your recovery capabilities, and use that to inform how much risk you can comfortably take. A simple farm jack (a.k.a. Hi-Lift) is extremely versatile and relatively inexpensive. Know how to use all of your recovery gear safely and know the weight ratings of things like straps, tow points, hardware, etc.
4) Med kit(s) - Similar to recovery gear, this is a huge spectrum. Bring at least a basic first aid kit and know how to use everything you bring. In addition to the absolute basics, like band-aids and medicines (asprin, advil, zyrtec, imodium, etc) I would also recommend at minimum always carrying LOTS of gauze (rolls and pads), some triangle bandages, ace wraps and a SAM splint. WITH TRAINING I would recommend bringing a C-A-T tourniquet, staged. There's a whole bunch of other medical bits, if you have the time and money, i recommend looking for a "Wilderness First Aid" class in your area. These are typically a weekend class and cost a few hundred bucks.
5) Communication plan - have at least one way to contact somebody in an emergency. In most areas in the US, a phone will get service if you get high enough - a summit, ridgeline, etc. GMRS and or ham radio is great if you know how to use them well and know the radio-scape of the area, using repeaters, etc. InReach or SPOT devices are more expensive, but very easy to use.
