UPDATE: merge and synonymisation complete.
You missed one:
parallel-universe with 54 questions. Since there doesn't seem to be any widely agreed-upon difference in meaning between "parallel universe", "alternate reality", and "alternate world", and they're usually if not always used to mean the same thing:
I propose that all three of these tags should be merged & synonymised.
If this answer gets sufficient support, a mod can do this without bumping any questions to the front page. Please leave suggestions in the comments as to which of the three tags should be the 'master' and which should be its synonyms.
(There's also an alternate-history tag. I believe "alternate history" may have different connotations and meaning to the other three - more about changing specific historical events than setting up an entire separate universe - but if I'm wrong, please do correct me in the comments and I'll edit the above to propose that all four tags should be merged and synonymised.)
Let's also take a quick look at the tag wikis. Some of them are better than others, and we need to decide which one(s) we want to keep elements from before doing the merge.
alternate-realities:
A reality different from that which is considered 'normal'. This normally occurs when timelines overlap and people/objects are transferred from one reality to another. E.G., consider the alternate reality in multiple Star Trek: The Next Generation episodes, including the alternate timeline of the final episodes 'All good things' - the events in all three timelines differ from what happens normally in the 'original' timeline.
alternate-world:
A fictional location. Sometimes known as a parallel universe.
Alternate worlds are usually similar to, but are noticably different than the worlds they are viewed from. They often serve as cautionary tales and sometimes take the form of an alternate timeline (possibly from the result of time travel paradox's), or as a reality in another dimension. Any distortion of past history, depending on the the observers point of view, could be considered an alternate world.
parallel-universe
A parallel universe or alternative reality is a hypothetical self-contained separate reality coexisting with one's own. A specific group of parallel universes is called a "multiverse", although this term can also be used to describe the possible parallel universes that constitute reality.
While the terms "parallel universe" and "alternative reality" are generally synonymous and can be used interchangeably in most cases, there is sometimes an additional connotation implied with the term "alternative reality" that implies that the reality is a variant of our own. The term "parallel universe" is more general, without any connotations implying a relationship, or lack of relationship, with our own universe. A universe where the very laws of nature are different – for example, one in which there are no relativistic limitations and the speed of light can be exceeded – would in general count as a parallel universe but not an alternative reality.
Fantasy has long borrowed the idea of "another world" from myth, legend and religion. Heaven, Hell, Olympus and Valhalla are all “alternative universes” different from the familiar material realm. Modern fantasy often presents the concept as a series of planes of existence where the laws of nature differ, allowing magical phenomena of some sort on some planes. One of the first science fiction examples is John Wyndham's Random Quest about a man who, on awaking after a laboratory accident, finds himself in a parallel universe where World War II never happened with consequences for his professional and personal life, giving him information he can use on return to his own universe.
Typically, parallel universes fall into two classifications. The first may be more accurately called a "diverging universe" whereby two versions of Earth share a common history up to a point of divergence. At this point, the outcome of some even happens differently on the two Earths and the histories continue to become more different as time elapses since that point, such as the star-trek-tng episode "Parallels". The second type is where despite certain, often large, difference between the two Earths history and/or culture, they maintain strong similarities. In such cases, it is common that every person in one universe will have a counterpart in the other universe with the same name, ancestry, appearance, and frequently occupation but often a very different personality, such as the star-trek-tos episode "Mirror, Mirror".
See also: alternate-history hyperspace sliders time-travel
Further reading
Source: Parallel universe (fiction) on the English Wikipedia.