There are three main possibilities. The universe will expand forever, the universe will contract, or it will reach a point of stability and neither expand nor contract.
Determining the correct scenario depends on finding the correct value for lambda, or the
cosmological constant. It is currently believed that the universe does not have enough
critical mass to cause a contraction and it will continue to expand indefinitely. Proponents of "
Big Crunch" theories typically argue that we have not calculated the correct value for lambda.
More technical info here:
How does the cosmological constant affect the evolution of the Universe?
