Around 2030–2036, the power will likely drop below the level needed to run even a single instrument. At that point, Voyager 1 will officially "die" as a scientific mission.
But Voyager will keep going forever.
Because there is no air resistance or friction in the vacuum of space, Voyager 1 doesn't need "fuel" to keep moving. According to Newton’s First Law of Motion, an object in motion stays in motion unless acted upon by an external force. Since there's nothing out there to stop it, it will continue its journey long after its systems go dark.
In 40,000 years: It will pass within 1.7 light-years of the star AC+79 3888 in the constellation Ursa Minor.
In 300,000 years: It might pass near the star Sirius.
The Long Haul: It is expected to orbit the center of our Milky Way galaxy indefinitely, potentially for billions of years, carrying the "Golden Record" as a final message from humanity.
Fun Fact: If Voyager 1 were to hit a pebble-sized object at its current speed, it would be catastrophic. Fortunately, space is so incredibly empty that the odds of it hitting anything larger than a dust grain for the next several billion years are nearly zero