There won't be a big crunch, the universe (well, our universe if you follow the multiverse principle) just simply continues to expand at an accelerated rate depending on what objects are being observed from our point of reference. What is our universe expanding into? Million dollar question if ever there was one. unlikely we will ever know the answer to this as human beings. The machines we send out to find those answers will likely know though in millions/billions of years to come.
The Universe might have an "end" in the standard sense, but we will never ever be able to see or get to it. There's a very simple reason for it, the rate of expansion the farther away galaxies get from us accelerates as time goes on relative to us. There comes a point where their distance is so great that they reach and exceed the speed of light as they move away from us. Of course the point at which the light they emit, the same light that eventually reaches us millions/billions of years later, carries on coasting through space at the speed of light, but as the universe expands, the physical galaxies themselves spread apart at their respective rates.
We just won't be able to observe those galaxies any more because the light stops reaching us since the point of reference that began has finished and the new point of reference would otherwise be from the galaxy drifting away beyond the speed of light.
It's quite confusing, but Ask an Astronomer explains it really nicely, well worth the read! But the main bit is here:
Source:
http://curious.astro.cornell.edu/97...peed-of-light-disappear-from-our-observations