We all know that our universe is inflating from what is known as the Big Bang. However, will our universe continue to inflate at the current rate? Or after reaching a maximum size, will it collapse in a Big Crunch?
While there is a general consensus aligned with the Big Bang theory's historical and current stages of the universe. To note, there are three theories with focus on this topic regarding the future, namely: the open universe, flat universe and closed universe theories.
Ultimately, the fate of the universe depends on the outcome of the competition between the expansion and pull of gravity.
The consequence of both of these is that the universe will eventually become a very, very dark and lonely place, with all galaxies, stars, et cetera, being so far away from any other, or burned out, with all original hydrogen used up; we can forget about our ancestors observing Andromeda, and the like - humans watching the sky would see nothing but blackness, voids in the distance.
If this is the case, the fate is a Big Crunch, where, as the universe contracts, galaxies fall inwards toward each other, wreaking catastrophe, until all matter is as it once was: crushed into an extremely hot, super dense state. There is also the oscillating universe model which is a variant that says another Big Bang would then occur, resulting in a brand new universe born out of the same matter.
What we have to understand is that the best model is the one that agrees best with observations (for instance, the Steady State theory contradicts observations and so is largely discounted.) It would be nice if we could observe the universe as it was billions of years ago, but alas, we can't do that directly. So, we use other methods such as looking at far away places in space at different distances - this way we can measure redshifts, but our instruments still aren't sufficiently evolved to provide precise measurements at such distances - now, the data used to check against cosmological models are wrought with uncertainties; this means we need still yet more information to fully determine which of the theories are correct.
The only definitive answer is maybe. Observations now seem to indicate that the Universe is dominated by dark energy, which leads to the most likely conclusion that the Universe will expand faster and faster, eventually resulting in the disappearance of everything that isn't bound to whatever object in which you reside. In the case of humans, that would be the Milky Way, the Local Group of galaxies to which it belongs, and the Virgo Supercluster, to which the Local Group belongs.
This is the one question that lies at the heart of all of cosmology, which is one of the hottest and most active areas of astronomical research, so stay tuned.