If we do wish to take the theory seriously, as we should since it is so powerfully accurate, then we are led to the Many-Worlds Interpretation as the most "face-value" interpretation.
Many Worlds? The Everett Interpretation
Universes of Another Kind
There are other kinds of multiverse that physicists discuss, but there's an entirely different kind of multiverse that is discussed by philosophers, not physicists. This is the multiverse of "possible worlds", and was introduced as a semantics that made modal statements much easier to analyse.
The Platonic Realm 