[ericsp23]

In the short term the biggest threat to our existence is nuclear or biological warfare, or envirmonmental collapse. We can reduce the threat to our existence by creating self-sufficient, off world settlements, either on other planets, moons, or asteroids, or man made settlements. By expanding a significant part of our population off of the planet our existence is no longer threatened by a planatery disaster. In fact the farther out we expand the more secured our continued existence becomes. If we can expand beyond our solar system we are no longer vulnerable to local stellar events. If we can expand throughout our entire galaxy, and even beyond it, then our continued existence is likely guaranteed for a very long time.
Unfortunately the fate of our universe is likely going to be our fate as well. There is no hard evidence that alternate universes exist, and even if they did, there is no known way to get to them. Thats not to say that will always be the case, anything is possible, but for now that idea belongs in the realm of science fiction.
The Big Crunch that is alluded to in the original post now looks like a very unlikely outcome. The two most likely scenarios, according to our current knowlege of cosmology, is the so called Big Rip, or heat death. The Big Rip is based on the recent discovery that the universal expansion is actually accelerating rather than slowing down. If the accelleration continues indefinitely then eventually all elementary particles will be flying away from each other at such a great speed that each one will exist in its own light cone and not be able to interact with any other particle in any way. Each particle would be its own universe essentially. Life as we know it could not exist under those conditions. Of course, that is still speculation. We don't know if the rate of acceleration will continue as it is now, speed up, or stop altogether, since we don't really understand what is driving it. So there is no way to know how close we are to this happening, or if it will happen at all.
The heat death scenario is the other possible scenario. If our universe is a closed system, and there is no evidence at this point that it isn't, then eventually there will be no free energy and entropy will be maximized. Since free energy is required for all known life processes, no known life could exist under thses circumstances.
Thankfully, neither of these scenarios is likely to occur any time soon. We will almost certainly not have to worry about anything like that for billions of years at least.