The idea of parallel universe is certainly an amusing one. Not only does it provide a rich and fertile field for storytelling, but it is alluring to wonder about what one’s life might be like under different circumstances (the whimsical “what-if crystal ball”). However, there is a misconception on what parallel universes would actually be like.
People think that the idea of parallel universes means that every possible outcome could exist. This is (theoretically) true, but to a limit. What is not true is that in a parallel universe you are the opposite gender, or that there is a universe in which people are dogs and dogs are people, or you are blue, or a chair, etc.
The idea of parallel universes comes from the idea that for every decision, there would be two or more possible choices. More technically, it means that for every atom (or even sub-atomic particle), it can take on a different position or spin than what it did take in this one. While that means a countless number of parallel universes, it does not mean that in one universe, dogs evolved to be people and keep humans as pets or that you are 10′ tall and green since there is no combination of actual changes that could have lead to that.
In fact, while it is generally accepted that the number of parallel universes would be infinite, it may actually be finite. For one thing, there are not an infinite number of particles, so that is one limit. If the universe turns out to not be infinite in size, then that also puts a limit to the number of possible different permutations (configurations of particles). Finally, there is a practical limit to the number of infinitesimal changes to position or spin that a particle can take. For example, an atom could move 1m, or 1cm, or 1mm, or 1µm, or 1nm and so on; however there is a physical limit to how small a unit of distance it can move (at least as far as we currently understand). As such, there could be a practical limit to the number of different universes that can exist (though it would still be unfathomably large).
It might be better to add the term possible to the term parallel universes. When discussing fantasy ideas of worlds where everything is upside-down or underwater and such, it would be more appropriate to use the term alternate reality instead.