Over the past four decades, since the episode "Mirror, Mirror" first aired on 6 October 1967, we have seen multiple iterations of the alternate reality known colloquially as "the Mirror Universe."
The Mirror Universe is best characterized as an amoral companion to the familiar, mainline Star Trek universe. Rather than the benevolent United Federation of Planets being formed by a willing group of human and nonhuman worlds, we find instead a brutal, totalitarian regime known as the Terran Empire.
In at least two variants of the Mirror Universe, the Terran Empire fell, thanks to visitors from the mainline universe--or, at least, a close enough approximation thereof, as the mainline group could not have been in two universes simultaneously--influencing the decisions of the Mirror Spock. In others, however, the Terran Empire did not fall. Additionally, the points of divergence for the various incarnations of the Mirror Universe appear to be significantly different. With multiple points of divergence, both pre- and post-contact with either the mainline universe or a near-identical iteration, one can only conclude that there exist multiple variations of the Mirror Universe.
The history of the Mirror Universe seen in The Mirror Universe Saga, published in 1985 by DC Comics, is significantly different from the history of the Mirror Universe seen in the Star Trek: Enterprise episodes "In a Mirror, Darkly," Parts I and II, which aired two decades later in 2005.
In Star Trek: Enterprise, the Terran Empire had existed for centuries before contact with extraterrestrials of any species. Initially bound to Earth, the empire spread to other worlds after the Mirror Zefram Cochrane and his followers murdered the crew of a Vulcan ship that came to investigate and make first contact following Cochrane's warp flight in 2063. Launching a surprise attack with the seized technology, Vulcan was the first of many worlds to fall. For simplicity's sake, I'll designate this MU1, as the divergence precedes that of the comic.
In The Mirror Universe Saga--which was originally published in issues 9-16 of the ongoing Star Trek title under the name "New Frontiers"--however, the crew of the I.S.S. Enterprise invades the mainline Star Trek universe shortly after the resurrection of Captian Spock on the Genesis Planet. During the course of the storyline, Kirk and crew incapacitate their Mirror Universe doubles and travel to said universe to mount a counteroffensive. While there, Kirk meets the Mirror David Marcus, who was a member of the anti-imperial resistance movement. Marcus revealed to Kirk that, in his universe, Earth lost the war against the Romulans. After decades of occupation by their oppressors, humanity overthrew the Romulans, and the Terran Empire was born in xenophobic vengeance, seeking to crush any aliens under their heel as potential enemies, so they would never be conquered again. This universe will be known as MU2.
Both of these universes would later encounter the crew of the U.S.S. Enterprise. The intent of the writers of the television episodes was that they were from the same universe as that depicted in the original Star Trek, so I will operate under the assumption that the Enterprise crew encountered in MU2 was from a universe that was nearly identical to the mainline universe, but subtly different; the results of the visits in both universes would produce the same outcome: each universe would spawn a minimum of three universes from the decisions of the Mirror Spock. Again, for simplicity, these will be either "A," Mirror Spock kills Mirror Kirk immediately upon his return to the I.S.S. Enterprise; "B," Mirror Spock waits for appropriate time to kill Mirror Kirk; or "C," Mirror Spock does not kill Mirror Kirk (this also has subvariants-C1, Mirror Spock attempts to kill Mirror Kirk, but fails; or C2, Mirror Spock does not attempt to kill Mirror Kirk at all).
With this nomenclature in mind, we have seen stories in nearly all of these variants. The Star Trek: Enterprise episodes are clearly set in MU1, as is the Star Trek episode "Mirror, Mirror." The comic "Fragile Glass," published in 1997 by Marvel Comics, is MU1A. The "mainline" Mirror Universe, as detailed in the overwhelming majority of the television episodes and novels, is MU1B1, as detailed in the anthology Glass Empires, and the story "The Sorrows of Empire." The Mirror Universe depicted in William Shatner's novels seems to be MU1B2, as Spock attempted to kill Kirk, who had by that point used the Tantalus Device to appoint himself Emperor Tiberius, and though he apparently succeeded (and the Empire later fell to the Klingon-Cardassian Alliance), Tiberius survived and went into hiding for nearly a century. It is likely that the Star Trek: The Next Generation novel, "Dark Mirror," which involves the crew of the Galaxy-class I.S.S. Enterprise NCC-1701-D, is from some variant of MU1C.
The Mirror Universe Saga, as previously stated, spawns from MU2, and must logically fall under MU2C2, as that version of Mirror Spock never attempted to kill his Kirk. The last we saw of that I.S.S. Enterprise crew, however, they were surrounded by Imperial starships, which were about to destroy their shuttle, believing them to be the mainline Enterprise crew, thanks to the earlier actions of that crew. This leads to two possibilities: MU2C2a, they are killed, or MU2C2b, they somehow survive. This question, however, has not been answered, as no further stories seem to have encountered this universe.
There is also another divergence in the timeline concerning the development of cloaking technology. When Bashir and Kira first encountered the Mirror Universe, MU1B1a, they are taken by surprise when a Klingon ship decloaks and escorts them to the Mirror Terok Nor. Several years later, however, Quark and Rom apparently travel to MU1B1b, which must be a different reality than the one most frequently visited by the other members of the DS9 crew, as in this universe, cloaking technology does not exist, though the political situation there is effectively identical.
In conclusion, it can be confidently stated that we have seen at least six distinct iterations of the Mirror Universe, given the evidence at hand.
To further clarify the MU1 "family" of Mirror Universe variants, I've created the following flowchart to illustrate the relationships between the realities and their points of divergence. [amazon_link asins='B01CJW334Q,B01N9BJHPI,B01N47VPJG,B07G2D87C1,B000NY126O,B000XPNVW6,B002WLCKFS,B004T4KRFQ,B000OV1BW6,160010522X' template='ProductGrid' store='harlander-20' marketplace='US' link_id='a8b5af96-0e5c-11e9-b6e8-bd464730aede']
To further clarify the MU1 "family" of Mirror Universe variants, I've created the following flowchart to illustrate the relationships between the realities and their points of divergence. [amazon_link asins='B01CJW334Q,B01N9BJHPI,B01N47VPJG,B07G2D87C1,B000NY126O,B000XPNVW6,B002WLCKFS,B004T4KRFQ,B000OV1BW6,160010522X' template='ProductGrid' store='harlander-20' marketplace='US' link_id='a8b5af96-0e5c-11e9-b6e8-bd464730aede']