The Universe could in fact expand forever... or it could collapse into the Big Crunch. This is influenced by how fast the galaxies are moving apart and how much total mass there is in the Universe. We can measure how fast the galaxies are separating quite easily by using ideas of red-shift. However, it is more complicated to measure how much mass there is in the Universe and if we knew that then we would be able to predict the future of the Universe. However, measuring how much mass there is in the Universe is a difficult task, seeing as most of the mass appears invisible, i.e. black holes, particles and other kinds of matter.

Depending on how much mass there is, there are two ways in which the Universe could go... if there is enough mass then we'll get the Big Crunch because if there is enough mass compared to how fast the galaxies are currently moving then the Universe will eventually stop expanding and begin to start contracting and therefore we would get the Big Crunch which would be followed by another Big Bang and then endless cycles of expansion and contraction...

However, if there is too little mass then the rate of expansion will slow down and the Universe will continue to expand forever. This means that the Universe would become more and more spread out into eternity...