In a closed universe, gravity will eventually
re-collapse the universe back into a dense point just like
how the universe started in the Big Bang model. And then the
Big Bang would occur once more, this process is also know as
a cyclic universe. In an open universe the universe will
continue to expand forever and due to the conservation of
energy and the 2nd law of thermodynamics the universe will
eventually end up in a 'empty' and dark state. Stars no
longer form since there is no more hydrogen or any material
is so far spread out that stars forming is impossible. Black
holes are one of the last things to exist but even then as
they radiate their mass away they will also eventually
disappear. It is also theoretically possible with some
theories that matter itself could dissolve, 'protons decay
into electrons, positrons, to neutrinos', this would occur
before the evaporation of all black holes. And this all
comes to an end in the Big Chill where the temperature of
the universe reach 0k and is in a basic sense empty.
Currently we are in a stelliferous age, an age
where stars are still being born. But once these stars stop
being born and eventually all die off (100 trillion years)
and then it will be the degenerate age which the universe
just becomes dark and everything not tied to the local group
will be further than one million mega parsecs.