I always thought at some point the universe would stop expanding and start contracting until all matter and energy was condensed into a singularity again. Time would not exist so there's no point wondering how long the universe would be in this state. Then at some point a new Big Bang would occur, although since time does not exist in between the Big Bang would occur at the exact moment the universe compressed to a singularity. The end of the old universe causes the start of the new universe. Endless cycle.
I don't know if this is supported by any current physics knowledge.