Say a photon left one of the first stars ever created in our universe. This photon has been traveling for 13+billion years through the vastness of space without ever hitting anything. Sure, it's probably been tugged at by gravitational interactions, but it's still happily traveling at the speed of light without direct interaction with matter.
As we know, most of the universe is composed of mostly empty space. The odds of any single photon hitting something (like the Earth as starlight, etc) would seem to be very small.
What will eventually happen to this photon? Will it eventually reach the other end of the universe, and if so, what would happen to it there?
"Will it eventually reach the other end of the universe"
The universe has no "edge". This may be strange and hard to grasp at first, but is quite interesting :) If you are curious about it, I suggest opening a question about the "end" of the universe in physics.stackexchange.com. $\endgroup$