Voyager 1, launched in 1977, has reached the edge of the solar system, 8.4 billion miles from the sun. NASA says the spacecraft and its trailing twin, Voyager 2, have enough fuel left to keep operating until 2020. What sort of fuel are the Voyagers running on?
The spacecraft actually carry two types of fuel—one to power the thrusters, the other to keep the electricity humming. The propellant is hydrazine, a simple concoction of nitrogen and hydrogen that smells like weak ammonia. It was chosen—and remains favored today—because it's cheap and has a very low freezing point. The Voyagers' jets are used to orient the vessels; the geek term for the hydrazine is "attitude control propellant." (There's no need for constant propulsion, of course, because space is gravity-free, so the initial boost went a long way; the spacecraft additionally took advantage of the outer planets' gravitational fields, which act like slingshots to increase speed.) NASA estimates that the Voyagers' fuel efficiency is upwards of 30,000 miles per gallon of hydrazine.
Voyager 1 has enough hydrazine to keep going until 2040, while Voyager 2's juice can keep it hurtling along until 2034. (Though the spacecraft are identical, Voyager 2 has had to expend more hydrazine visiting Uranus and Neptune.) The real limiting factor is the other fuel, plutonium-238 dioxide. This is what powers the Voyagers' scientific instruments and communications equipment. The plutonium is converted into electricity by onboard radioisotope thermoelectric generators (RTGs), which feed off the heat generated by the radioactive fuel's decay. The fuel spheres are encased in a special iridium alloy, to prevent contamination in the unlikely event that the Voyagers crashed shortly after takeoff in 1977.
The plutonium's radioactive decay means that the fuel is generating less and less heat as the years go by, and consequently the RTGs are producing less and less power. At launch, the RTGs were cranking out 470 watts worth of electricity; now it's more like 315 watts. NASA is trying to combat the problem by shutting down non-critical systems, and alternating which instruments are on and off. But come 2020 or so, there won't be enough plutonium left to keep the heaters working, and everything of value will shut down.
Explainer thanks Slate reader Rosa Garcia for asking the question and Dr. Edwin V. Bell of the NASAGoddardSpaceFlightCenter for helping to answer it.