You should never travel on rural roads without a verifiably working satellite radio (or personal locator beacon) in the worst case scenario. For communication, I travel with my main cell phone, a backup cell phone / wireless hotspot with a completely different provider (T-Mobile + Verizon, lately), a satellite communicator (several links posted in this thread that will work just fine), flares and high-intensity LED road lights that have constant + SOS flashing patterns, two high-intensity flashlights, and a high-powered green laser pen for alternative forms of signaling.

Additionally, you should obviously carry plenty of food, potable water, basic medical supplies including a round of antibiotics, tire inflation/repair devices, a multipurpose sharp knife, two long-lasting external batteries for your USB devices that can also jumpstart a car (super cheap on Amazon, surprisingly), and potentially a firearm if you're into that kind of thing and trained to use it. Standard prepper checklists will work here.

It sounds like a lot, but even semi-rural travel 15-20 miles off marked and standard roads are dangerous as hell, as this story and others clearly can show. You will almost certainly never need all of your equipment, but if you travel even occasionally, you will absolutely need some of it - and you won't be able to predict which piece of gear you do need. It's about being prepared for a wide variety of events, not one severe event.

Nature doesn't cooperate.

EDIT: Forgot, pack a basic set of tools: Screwdriver with various bits, socket wrench (ideally with an extension), car jack, pliers, length of wire, length of rope, aim-and-flame extension lighter (vastly preferred to a handheld cigarette lighter and not any more expensive; get a flexible shaft if you want to be fancy and shell out an extra $2), tire iron (add a breaker bar, probably), and a stack of kindling, which can simply be a bunch of old or free newspapers.