As of now, we don't have the slightest clue as to what Omega is because it depends on entirely Universal quantities that may be impossible to measure. Some theorize that 90% or more of the Universe's mass is made up of dark matter, which does not reflect light and is thus not observable using telescopes of any form. Many think of dark matter as some kind of mysterious pseudo-substance, but it could be as simple as billions and billions of burnt out cinder-cores from pathetic star deaths. Some stars explode into supernovae at death, others collapse into black holes. But the largest majority simply burn out, potentially (eventually) reaching a state of death, where all that remains is the fused metal center.
The Omega Constant was appropriately named for the purpose of understanding the fate of the Universe. If the Universe is relatively dense, then Omega is greater than one (even if it only equals 1.00000{billion 0s}1), and the force of gravity will eventually overcome the force(s) that is/are expanding the Universe. As of now (and for the next thousand, million, billion?) years the Universe is actually accelerating apart, theoretically by a cumulative force exerted by virtual particles that occupy the "empty space" between galaxies, a volume that grows exponentially in "emptiness" as the galaxies move apart from each other in very large, quantized amounts.
If Omega equals one (meaning 1.{infinite zeros}), meaning the Universe has the exact amount of matter density to equal its critical density, then it is just dense enough to continually expand, approaching forever in time (at a decelerating rate), asymptotically seeking a state of infinite volume. This is "the heat death of the Universe," see this node as well for details. Note the language used in describing this – "asymptotically" and "approaching forever at a decelerating rate." The next situation is far different, although it initially may sound the same. If Omega is one, then heat death should never actually be reached.
If Omega is less than one, the Universe will expand forever. But this time there's no gradual deceleration, no "approaching forever" -- if Omega is less than zero than the Universe will expand forever, and will reach infinite volume, and will reach a state of heat death. In other words, it will continually accelerate apart, rather than slowing down. No "approaching zero," or "approaching infinity." It defines infinity, and redefines it continually, until it has nothing left to burn. As of now, it appears that this is the Universe we live in. This could change, but as of now, 10-20 billion years from the flash that created all of this, it still seems to be exploding. The big bang isn’t a single event. <opinion>The big bang is the Universe in which entropy is always increasing, due to exponential increases in volume.</opinion>
What I Think (factual part ends here)
I personally believe that Omega is either less than one or greater than one, as either of these situations supports my philosophical position of "eternal recurrence," the idea that this same exact life will be lived again infinite times, even if only occurring one time out of every five googolplex ^ googolplex Universes. If Omega is less than one, the Universe will collapse, and will probably expand again and repeat this cycle forever. Collapsing allows it to conserve all of its energy, probably forming the all-massive true singularity that makes the big bang possible.
But if it expands forever, constantly accelerating apart, reaching infinite volume, then at some arbitrary point we should reach a state of "nothingness," akin to the nothingness that the big bang supposedly came from and destroyed (more likely, transformed, or infused). If every galaxy is constantly pushing away from every other galaxy, and every star is eventually going to die, then we should reach some place where every bit of matter and energy has been converted into entropy, into the effect behind the forces that stretch the cosmic fabric of space, as if warping by the hot energy constantly emanating from every massive point in the Universe!
I believe that a collapsing Universe is not necessary in order to have a repeating Universe. And if I’ve existed in one iteration, than there have to be others, including one that is completely identical in every way to this one (thanks in part to Chaos Theory). And even if Omega does equal one, who’s to say the Universe doesn’t have the patience? As human beings we’ve never witnessed infinity or true nothingness. But the entire mathematics of Calculus is about how to manipulate limits to "approach infinity" and find answers to problems that would otherwise result in division by zero, "0/0", or a "wrong zero" that should actually cancel out to one. This is what unifying the forces is all about; finding Calculus equations that remove the impossible elements from the problem, in order to solve what appears to be impossible and even nonsensical.
We can get around the problem with infinity with a little imagination and practice, so why can’t the ever-expanding-all-massive-all-powerful Universe? I think it’s even a little arrogant to think that this is the only cycle – that we are just lucky in being around to witness the one-time-only event that is the expanding Universe. Stars (although open systems) may represent the most accurate microcosm of the Universe – some of them explode, some of them collapse, but most of them burn out, reaching what is similar to a state of "heat death." Perhaps this Universe is merely a point on a grid of infinite other possibilities, all occurring simultaneously, but as a whole, the entire grid is truly "the Universe," and in order to conserve energyFor matter and energy to truly be conserved, there can be no "heat death" of everything. But that’s just my opinion (and first Nietzsche’s), I could be wrong.