Somebody correct me if I'm wrong, I don't know a whole lot on this subject, but..
Omega, the ratio of the observed density of the universe to the criticle density of the universe (the density required to stop the expansion), is the deciding factor in the fate of the universe. If omega is less than 1, the universe will keep expanding. If it's greater than 1, the universe will slow down, and start to contract, the "ending" would be the "Big Crunch." If omega is equal to one, the universe will stop expanding, but will not start to contract.
The reason I have "ending" in quotes is because some believe that after the "Big Crunch" another "Big Bang" will occur, and the cycle will be started all over again.