In town, something breaks and you call someone. In the country, the someone is two hours out and charges for the drive. These are the systems worth understanding before they fail, because they fail on the coldest night of the year.
Water
Know where your well head, pressure tank, and shut-off are, and label them. Learn what your pressure switch sounds like when it is working, so you notice when it is not. Short-cycling — the pump kicking on and off rapidly — usually means a waterlogged pressure tank, and left alone it will destroy the pump.
Keep a spare pressure switch and a roll of pipe thread tape. Know how to drain the system before a hard freeze if the power is out.
Power
Outages are longer in the country and nobody is coming quickly. Know which breaker feeds what, keep the panel labelled, and keep a headlamp somewhere you can find it in the dark. If you run a generator, run it outdoors and far from windows, always, without exception — carbon monoxide kills people every winter who thought they had enough ventilation.
Heat
Have the chimney swept and inspected before the first fire of the season. Keep the stove gasket sound and the flue clear. Store a season’s fuel before you need it, not during the first cold snap.
Septic
Pump on a schedule rather than after a backup. Know where the tank and lids are and keep them accessible. Nothing goes down the drain that did not come out of a body or a food, and no vehicles park over the drain field.
Vehicles and small engines
Learn to change your own oil, air filter, and spark plugs. Keep fuel stabiliser for anything stored over winter, and drain carburettors on equipment sitting idle. Stale fuel causes more small-engine failures than wear ever does.
The kit worth keeping
Adjustable wrenches, channel locks, a socket set, a cordless drill, a hacksaw, pipe thread tape, assorted hose clamps, electrical tape, a multimeter, a tarp, and a length of rope. Most emergencies are held together by something on that list until a proper repair is possible.
Know your limits. Gas lines, main panels, and structural work are for licensed people. Knowing which jobs are yours is part of the skill.