The shape of the universe is determined by a struggle between the momentum of expansion and the pull of gravity. The rate of expansion is expressed by the Hubble Constant, Ho, while the strength of gravity depends on the density and pressure of the matter in the universe.
If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the “critical density” which is proportional to the square of the Hubble constant, then the universe will expand forever. If the density of the universe is greater than the “critical density”, then gravity will eventually win and the universe will collapse back on itself, the so called “Big Crunch”.
However, the results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the “dark energy”.
If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.