As a relative dummy, I've greatly enjoyed re-reading by Max Tegmark's essay for Scientific American on parallel universes:
The scientific theories of parallel universes...form a four-level hierarchy, in which universes become progressively more different from ours. They might have different initial conditions (Level I); different physical constants and particles (Level II) or different phyical laws (Level IV). It is ironic that Level III [quantum many worlds] is the one that has drawn the most fire in the past decades, because it is the only one that adds no qualitatively new types of universes.
...Should you believe in parallel universes? The principal arguments against them are that they are wasteful and that they are weird. The first argument is that multiverse theories are vulnerable to Occam's razor because the postulate the existence of other worlds which we can never observe.
...But an entire ensemble is often much simpler than one of its members. (This principle can be stated more formally using the notion of algorithmic information content)...Similarly, the set of all solutions to Einstein's field equations is simpler than a specific solution.
...A common feature of all four multiverse levels is that the simplest and arguably most elegant theory involves parallel universes by default.