Voyager 1 and Voyager 2 - Wow!

mfb

We have ~10000 stars closer than 100 light years, giving an estimated star density of 0.0024 stars per cubic light year. As an upper estimate, I'll use 0.01~1/125 here. Few stars have a radius larger than ~750 times the solar radius (500 million km), so this is a very generous upper estimate for a typical star. It also accounts for the gravitational attraction, which increases the impact probability. Planets and other massive objects are completely negligible here. With those numbers, we have (on average) one star with a radius of 500million km in every cube with a side-length of 5 light years. This star occupies a fraction of 3.5*10^-10, leading to a mean free path length of 14 billion light years, assuming the Voyager probes stay in a region with similar stellar density (they should orbit the galactic center in a roughly circular orbit like our sun). With a relative velocity of ~50km/s, this leads to a mean "lifetime" of ~10¹⁴ years, or about 6000 times the current age of the universe.

The Voyager probes will see all sorts of decay due to radiation, dust and so on - but they will not collide with any massive object within any reasonable timescale and probability, assuming they are not captured on purpose.