Recently it's been reported at Slashdot that a mathematical answer to the question of parallel universes exists.
(They used the word "mathematical", which should have been my first clue that I shouldn't be reading it. "Mathematical" means "I'm trying, and failing, to use math".)
Anyway, a bit of combing through the Slashdot comments turned up this article and this one from New Scientist. It seems reasonably clear that somewhere there is some work, and what this work purportedly shows is that the many-worlds interpretation of quantum mechanics is consistent. One of the articles I found said that the work was done by David Deutsch, David Wallace, and Simon Saunders, and was presented at a conference at the Perimeter Institute for Theoretical Physics; I think that the articles are referring to this talk by David Wallace, but they might be referring to a talk by Saunders at the same conference.
Basically, what the many-worlds theory says is that parallel universes are constantly branching off of ours whenever any sort of observation occurs, therefore causing the collapse of a wavefunction.
Of course, events like those are happening all the time. Where are these parallel universes? And I'm not even going to try to think about how many of them there are, because the number is obscenely ridiculous. How many wavefunctions are collapsing around you right now? And the whole structure is branching. Let's say that every second, somewhere in the universe, exactly one wavefunction collapses, and there are two possible pure states that it could collapse to. The universe is about 5 × 1017 seconds old, so the number of universes you'd need to make this work is two to that power. Occam is rolling over in his grave. Except maybe in the universe these people are in, Occam never existed.
Besides, we can't see these other universes. Isn't that convenient? Perhaps the two major interpretations of quantum mechanics -- the probabilistic interpretation and the many-worlds interpretation -- are just two different formalisms for understanding the same thing. It's easy to picture this giant combinatorial tree of universes; it's harder to picture superpositions.
You're offended by the idea that "God plays dice with the universe". So you call zillions of other universes into existence because you can't handle it? Einstein would be ashamed.
(Edited, 12:37 pm: today's Questionable Content refers to the many-worlds interpretation.