There have also been various novels which were set in the mirror universe, although for various reasons they don't all fit in with each other or with the actual TV episodes. I like to think that there are several alternate universes which diverged after the original transporter accident.
Recapping the key points from the TV episodes, when Kirk visited the mirror universe he found that Spock was "a man of honour in two universes". So, he persuaded mirror-Spock that he should institute reforms, and make the Terran Empire more like the Federation. In DS9, we find that Spock was successful, but at a cost: 100 years later, the other galactic powers have moved in, and Terrans (humans) are now treated as slaves by the Klingons, Bajorans, and Cardassians. As I mentioned a while back, one of the DS9 writers said that they were trying to deconstruct the original story. He gave the parallel of the Roman empire, which was brutal, but was afraid of the barbarian hordes outside (ditto for the Chinese empire and the Mongols); it's fine to say "let's all be nice", but then you're no match for your enemies.
The first book was the TNG novel "Dark Mirror", by Diane Duane, published in 1993. This was written before the first relevant DS9 episode, so it was just following up on the TOS episode, and it was an opportunity to explore the same premise with a new group of characters. In this story, the Terran Empire is still going strong, and they have their own version of the Enterprise-D; the idea is that the mirror-Spock was killed after he tried to make changes, so Kirk's visit didn't really change anything. (As with many fanfic stories, this book provided an excuse to put Wesley Crusher in the Agony Booth.) I enjoyed this story, and I've read it several times.
Apparently three of the "Shatner-verse" books ("Spectre", "Dark Victory", and "Preserver") were set in the mirror universe, but I haven't read any of them, so I can't comment on their quality.
Next came the "Dark Passions" duology (i.e. a story spread across two books) by Susan Wright. This was published in 2001, i.e. after the DS9 episodes but before the Enterprise episodes. These books were set entirely in the mirror universe, and featured female characters from TNG, DS9, and Voyager. They were described as being "sapphic", the implication being "Trekkie babes in hot lesbo action!" However, the first book was actually quite restrained on this issue (I haven't read the second one). The basic premise is that Annika Hanson (7 of 9) is a secret agent, and at the start of book 1 she goes off to infiltrate the Klingon empire; I was amused when she compared this to performing Shakespeare, i.e. exaggerating all the emotions. All in all, I'd say that the first book was worth borrowing from the library, but I'm not sufficently interested to actually pay for book 2.
More recently, there's been a DS9 relaunch in book form; the idea is that this picks up where the TV series left off. The most recent novel ("Warpath") was published in 2006 and ended on a cliffhanger which involves the mirror universe; presumably the next novel ("Fearful Symmetry") will follow up on that, although they've changed the author and delayed it until 2008.
In the meantime, there were two books published this year ("Glass Empires" and "Obsidian Alliances"), both of which were set entirely in the mirror universe. Each book is an anthology containing three novellas, so that's six stories altogether, one per "franchise" (Enterprise, TOS, TNG, Voyager, New Frontier, and DS9). These are a bit of a mixed bag, but on the whole I recommend them. They're consistent with all of the TV episodes, but not with any of the previously published "mirror universe" novels. (They're implicitly consistent with the DS9 relaunch novels, but that remains to be proven.) Taking the six stories in order:
* "Age of the Empress" (Enterprise), by Mike Sussman with Dayton Ward & Kevin Dilmore. This begins almost immediately after "In A Mirror, Darkly" (also written by Sussman), so if you haven't watched those episodes recently then you'll probably be a bit lost, since there's not much of a recap. At the same time, I get the impression that the prologue was tacked on after the rest of the story had been written. For instance, when the prologue refers to the Defiant, it says "And what of this vessel's original crew? According to Phlox, they had killed each other in a fit of madness - a century in the future, in an entirely different reality." In chapter 1, it says "It was true that the rebels [...] had aborted their planned attack on Earth, thanks to the timely arrival of the starship from the future and, incredibly enough, a parallel reality." It's not that incredible if you can hold your attention for 20 pages... I suspect that this is an effect of having several writers associated with a short story. Beyond that, the basic storyline is that the mirror-Enterprise crew are fighting each other like cats in a sack; since they're all basically scum, I found this pretty boring, because I didn't care which of them lived or died. It's possible that I'm being hard on this story because I didn't like the TV series much, so I'm not particularly attached to the mainstream universe counterparts, but all in all I'd say that you could skip this story and not miss anything.
* "The Sorrows of Empire" (TOS), by David Mack. This is probably the best of the bunch, since it has quite an epic quality to it. It spans a 30 year period, beginning just after the TOS episode and finishing just after Star Trek VI: The Undiscovered Country (or rather its equivalent), and we see how familiar events played out in a different way. It begins with Spock killing Kirk, and I think that Mack handled this well: he went into enough gory detail to make it clear that this kind of violence is unpleasant, not something to glorify, while still maintaining that it was necessary. Beyond that, this story takes an interesting approach, by deconstructing the deconstruction of the DS9 episodes! It's reasonable to say that changing the Empire would make them vulnerable to their enemies, but it's also reasonable to say that Spock is intelligent, and that he should have been able to anticipate that; according to this story, he did, and he deliberately allowed it to happen as part of a larger plan. (It's implied that this would come to fruition in the "near future" relative to the DS9 episodes, so there's scope for another story that follows through on this.) Mind you, this story didn't refer to the alien probe from Star Trek IV, and I'd be interested to know how the Terran Empire handled that one (assuming that they'd also driven the whales to extinction). So, I strongly recommend reading this story; it's worth buying the book just for that.
* "The Worst of Both Worlds" (TNG), by Greg Cox. This is a bit different to the other stories, since it focusses almost entirely on Picard; that's fair enough, since arguably it's a bit of a stretch to have the same group of people meeting up when history has diverged so much, and "Dark Mirror" included most of the crew. Like the TOS story, this has alternate versions of some familiar events (from TNG episodes), and it involves a conflict with the Borg, but ultimately it all seems inconsequential. If you have the book, you may as well read this story too, but I wouldn't go out of your way for it.
* "The Mirror-Scaled Serpent" (Voyager), by Keith R.A. DeCandido. This is set in the Alpha quadrant, the idea being that Neelix and Kes were sent into the Badlands rather than Janeway and co being pulled into the Delta quadrant. It's basically what I'd expect from KRAD, i.e. a good solid story, which would have worked well as an episode (or two).
* "Cutting Ties" (New Frontier), by Peter David. This runs a very close second to the TOS story, as I'd expect from PAD. I think it works well in two ways: if you've read the previous New Frontier novels (all of which he wrote) then it's good to read another installment, even if it is in another universe. On the other hand, if you're new to the characters then that doesn't matter because this doesn't rely on any previous stories (e.g. TV episodes), being in a separate area of the Alpha quadrant; hopefully after you've read this, you'll want to read the "mainstream universe" novels.
* "Saturn's Children" (DS9), by Sarah Shaw. This is a decent story, although you really need to have seen all the relevant DS9 episodes in order to follow it; there's a brief recap of what's happened since "The Emperor's New Cloak", but no more than that. Anyway, it does a good job of continuing the storyline from the episodes, as well as making a few changes that will probably be relevant in the next DS9 relaunch novel.