We have spent years traveling the back country in both deserts and mountains. There are a few things that make for a pleasant trip and a few others that have proven handy when problems arise. This list covers items that work for us. You may find a need for more or less but keep in mind that traveling the back country by definition means that you will be away from help if you need it. Be prepared to take care of yourself should you get stuck for at least a couple of days. Remember, cell phones will not work where there are no towers close by or the signal is blocked by mountains. So lets see what we have found to be helpful.
Make sure you have enough GAS for the trip plus extra. Do not count on there being gas stations open or even still in business in some of the small towns on maps. I have seen billboards advertising gas and when you get to the town, the gas station has been out of business for months.
You need good tires to travel most of the back country dirt roads. This doesn't mean you need giant off-road tires but it does mean that your tires cannot be bald and they should be inflated to the proper air pressure. Always carry a JACK to change the tires. I have gotten a flat far from help even with good tires. So be prepared to change a tire. Even graded dirt roads have sharp rocks which can weaken or puncture the sidewall of a tire. Check that your radiator isn't leaking and has enough coolant. There are obviously many more things to watch out for but this covers the basics and it is amazing how many people will ignore even these and end up in trouble. Many people would include at the minimum, a small toolbox and I actually carry a fairly good assortment of tools. One of the handier items is either a hand pump or one of the small electric compressors. These can be a life-saver if you find a tire including the spare, to be low on air.
Most people will carry snacks and something to drink with them but few think to carry REAL food just in case they get stuck. Now, you can argue what constitutes real food at home but when you are far away from the nearest store any can of beans will look mighty good should you be stuck for a day or two. I once tried to cross what turned out to be a deeper than expected river in Arizona only to get stuck half way across. I had my dogs with me and was over 50 miles from the nearest town. I wasn't even sure of my exact location but I wasn't much bothered by the problem because: 1) I had canned food to last me about a week. 2) I had a small bag of dog food for the dogs that would last them about a week also. 3) I carried over 5 gallons of water to drink. 4) This is VERY IMPORTANT, I had let someone know the approximate area I had gone to and when I expected to be back. If I did not call to report that I was back safely, they would have called the appropriate group (such as a local search and rescue team) to try and find me. For more on this little excursion see Stuck in the Bill Williams River. I was stuck in one of the few places in the desert that had a good supply of water (a river) and I carry a purification product with me most of the time. Do not attempt to drink water from any source in the back country without first purifying it in some way. Although people may not have polluted it, animals do not take the same precautions. I have drank water from within a couple of feet of a remote spring only to fall victim to the dreaded Montezuma's revenge while still out on the trail (within less than 30 minutes of drinking the polluted water). This spring, as many are, was polluted by wild burros in the area. Always, purify water when in the wild.
Hopefully no one ever needs a first aid kit but accidents do happen. Band aids and some type of antibiotic ointment is the least that you should have. Cuts, stings, and scratches seem to happen to everybody. Although there is controversy surrounding the use of a "snake-bite" kit I (and many people I know) still carry one. The controversy concerns the possibility of an infection from the kit's procedure of opening the wound. If a Mojave Green rattlesnake bites me when I am far from the nearest doctor, I will probably take the chance of an infection. A bite from any other rattlesnake would still be of concern, but I would probably try to get to a doctor first.
I started carrying a GPS unit a few years ago and don't go anywhere without it anymore. Besides figuring out where you are, you can also find the exact road you are looking for when you can't find it by using a map. One of the newer units from Garmin includes a two-way radio and a GPS locator. Don't forget the flashlite AND spare batteries. How about the matches? Don't forget those. You may not need them to cook but for heat, light, and a signal they can come in awful handy.
Always carry up to date maps but do not be surprised if they don't accurately portray the back country you are in. Topos maps are good for seeing the older roads and trails in a given area. Because of the time between surveys and printing, they are not very accurate regarding newer roads. The most common map sets that I carry are the State Atlas and Gazetteer topo maps by DeLorme Mapping. They are available for most states and are easy to carry and read. The newer versions provide GPS grids that can definitely help to locate places. Again, these are not perfect for locating roads. I once spent a couple of hours trying to find a road in northern Nevada only to decide that it didn't exist where the map showed it. Even the USGS can be wrong like the time I pointed out to them that they had inadvertently missed an entire mountain range in Southern California called the Calumet Mountains.