GO PREPARED
Things can and will go wrong out there, so always go prepared to spend a night or two. On the supplies side, the basics of backcountry driving are already on the packing list of experienced outdoors enthusiasts: maps, compass, extra eyeglasses and keys, a good first-aid kit, binoculars, trash bags, matches, clothing for inclement weather, hats and sunscreen, insect repellent, blankets or sleeping bags, flashlights or headlamps and extra batteries, plenty of food and water (a gallon per person per day is considered the absolute minimum) and something that will make you easy to spot should someone have to come looking for you. Don't forget to augment your supplies with enough nonperishable food and water for a couple of days in case you get stranded.

Here are some more auto-oriented things to bring:
1. A topped-off fuel tank. Fill up before every backcountry drive, every time. You will use your vehicle’s low gears much of the time, which will mean much higher fuel consumption than during on-highway driving. Unless you’re traveling for an extended period in a particularly remote area, it shouldn’t be necessary to carry extra fuel. If you do, strap a full can to the exterior of the vehicle, preferably the roof. Fill the can so that dangerous fumes won’t build up inside. Don’t use it until you’re sure your tank will take it all.
2. A shovel. Mine has been a life-saver and is the single most useful tool I carry. Yours will be, too.
3. Traction aids. You're going to encounter soft sand, and if you get stuck, your tires are going to need help. Metal "sand ladders," flat lengths of aluminum designed to give tires a firm surface, are available. You should bring two rolled-up strips of heavy carpet, each wider than your tires and about three feet long. Put holes in the ends, and if you need to use them, connect them with lightweight rope to the back of the vehicle. Then, when you drive off, they will follow.
4. Good all-terrain tires; a good (and properly inflated) spare and jack; a small board to support the jack on dirt; a couple of cans of pressurized tire sealant (available at department and auto-parts stores); a source of compressed air, such as a small electric air compressor that plugs into the cigarette lighter, or a tank of compressed CO2 and an air hose long enough to reach each wheel; a tire pressure gauge and even tire chains for mud and snow. Be especially careful in old mine sites and ghost towns, which are often littered with old, rusty nails.
5. Some basic tools, including a folding saw, jumper cables or stand-alone, battery-powered jumping device, duct tape, electrical tape, baling wire, spare fuses, multipurpose knife, high-strength tow strap, fire extinguisher, and a plastic sheet to put on the ground. An assortment of screws, washers, nuts, hose clamps and such could come in handy as well, especially if you're driving an older or modified (meaning trouble-prone) vehicle.
6. A portable tabletop gas barbecue. Sound extravagant? Your call, but it's quick and convenient and I never leave home without mine securely strapped to my roof rack.

I keep much of this stuff ready to go in large plastic storage containers. It's also important to secure your cargo so that it doesn't get tossed about on rough terrain. Sometimes, I bring my mountain bike as a backup vehicle. I occasionally use it to check out places that I don't want to drive to. The problem is that the sometimes severe side-to-side pitching caused by rough roads can break a bike loose from a rooftop mount.

These days, a cellular telephone can be handy, too, although I've found that they often don't work in the wild. Satellite phones can be rented at increasingly affordable rates, if you really need to stay in touch.