Well, that depends what you mean by "universe"!
Usually, when we talk about the universe, we're
referring to the visible universe - that is,
everything we can possible see or detect via
observations and experiments. In that case, we
don't know if there's more than one universe, and
we'll never be able to know because by definition,
we can't see anything except our own universe!
But if you can't detect something, even in
principle, does it make sense to ask whether or
not it exists? You see, you've stumbled on a very
interesting philosophical question of what it
means for something to exist!
However, there are some theories of physics
(like string theory) that say that our universe
could be one of many possible universes, and that
even though all the stuff we see is stuck in our
universe, different universes can pull on each
other gravitationally. That means that even
though we can't see matter in other universes,
maybe we could detect them by their gravitational
tug on us. In that case, we could talk about the
existence of other universes, but we simply don't
have any evidence that they exist.
The origin of the word "universe" is Latin:
uni=one and verse=turned. Together this creates
the concept of everything rotating as one. So,
rooted in the word itself is the understanding
that there is only one universe, and we use the
word to describe everything that exists that we
know about and even beyond that into the unknown.
In that sense, there is only one universe, there
is only one 'everything'. People sometimes talk
about an alternate universe or similar kinds of
terms, but so far we know of nothing else outside
of the thing that we have named the universe. It
really is all-inclusive.
There are theories that have hypothesized the
existence of other universes. For example, the
many-worlds interpretation of quantum mechanics
suggests that we exist as part of a multiverse,
where there may be a finite or infinite amount of
other, parallel universes to our own. This is not
something we can really test (at least not with
the technology we have now), so for now, this idea
remains a hypothesis.