Alternate Heresy
The Horus Heresy is one of the biggest events in the Warhammer 40,000 story. Naturally, people like dreaming up alternate scenarios. Page still being expanded.
The Dornian Heresy
The Dornian Heresy was the 40K web forum Bolter & Chainsword's project to switch the allegiances of the various Primarchs during the Heresy, and explore what would have happened to the Legions under their command if they had fallen or not.
Unlike the following scenarios, which were largely thought exercises in random threads on /tg/, this was a full project, with accompanying Index Astartes articles and quite a bit of fluff, which can still be found quite easily.
Essentially, during the incident on Davin, Magnus the Red actually arrives to visit and exorcise the infection on Horus instead of relying on Erebus' rituals. While successful at both saving the warmaster's life and preventing him from becoming corrupted, it did leave him out of commission. Following their temper tantrum, the Chaos Gods decided that the next best choice was Rogal Dorn, who had been going on overdrive with his pet pain glove.
In the end, the Space Wolves fell to Khorne, the Blood Angels fell to Nurgle (surprising, given the actual novels imply that they would've fallen to Khorne, if anyone (actually makes a lot more sense, SW hates psykers like Khorne, and Baal is an iraddiated waste)) the White Scars fell to Slaanesh in an event almost identical to the canon Death Guard,, the Raven Guard fell to Tzeentch, the Salamanders fell to Malal, and Rogal Dorn himself was the arch-traitor, with his Imperial Fists supporting Chaos Undivided (renaming themselves the Black Legion after the failure of the Heresy). The Ultramarines did not fall to Chaos, but instead became Reasonable Marines; they seceded from the Imperium alongside much of the Ultima Segmentum, and now exemplify progress while fighting off the Tau. The Iron Hands seem to have gotten mixed up with the Necrons, while the Fallen Angels won out over the loyalist Dark Angels.
On the Imperial side, the Word Bearers became the Ecclesiarchy (with no Kor Phaeron to twist it all to heresy - he proved incompatible with the gene-implants), the Iron Warriors remained siege masters, the Sons of Horus became the crusading Black Templars (after almost identically disowning Horus' foolishness which led to him being the new Sanguinius), the Emperor's Children remained exemplary perfectionists (except for Fabius Bile, but he's dead now... maybe), the Thousand Sons became blind psychic warriors (see: Grey Knights), the Death Guard became the core of the Inquisition, the World Eaters became serious instead of angry, the Night Lords remained loyal Scary Marines, and the Alpha Legion were just as sneaky and just as anti-Ultramarine, but still loyal (apparently the Cabal wasn't that convincing in the Dornian Heresy).
How the Space Marines are organized is also flipped, as the legions falling to Chaos occurred because of them being separated by all sorts of circumstances, so Abaddon (who takes over as leader of the Imperium after the Emperor's battle with Dorn) organized the legions into a few giant armies (by Space Marine standards).
It's pretty awesome...except that, as most alternate heresies are wont to, it all amounts to some absurd amounts of marine-wank. Perhaps the most particular is the Reign of Blood, where the Sisters of Battle never existed, because they were wiped out by the Word Bearers when they were still the Brides of the Emperor, and Goge Vandire (who was now the new Chapter Master following Lorgar becoming a martyr post-heresy) wasn't overthrown by some simple preacher, but by a novice marine named Sebastian Thor. Meanwhile, all of the xenos factions are left to mere footnotes or mentions (just as Games Workshop intended) and the impact this has had on the Imperium at large is left to interpretation.
The Imperial Heresy
In the Imperial Heresy, the God-Emperor of Mankind decided "if you can't beat 'em, join 'em" and sided with the Gods of Chaos.
The Eldar Gambit
In the Eldar Gambit, Eldrad meets the Emprah the day before the final assault on the Vengeful Spirit, offering assistance in exchange for closer Eldar - Human cooperation later.
The basis of the pact is that instead of taking the mortal blow that Horus throws at him on accident, he does it deliberately, and uses the energy of his own death to attack the Chaos Gods directly, specifically Slaanesh. He steals the stomach of Slaanesh and incorporates it into himself, so now all Eldar souls will go directly to him when they die, keeping them safe from the depredations of Chaos.
The thread was mostly speculation on how a united Imperium of Man and Eldar Empire would work together... and it's actually pretty awesome. Ollanius Pius being revered by guardsmen as an Avatar of Khaine and killing Horus right after Horus defeated the Emperor (albeit he was weakened from fighting the Emperor), Space Marines with soulstones to keep the forces of Chaos away from loyal marines, a fractured Adeptus Mechanicus (with four factions - Traitor, Loyal, Machine God fanatics and Fundamentalist (doesn't use Eldar tech that is now more freely available)), and more.
The Hektor Heresy, AKA the /tg/ Heresy
/tg/ Creates an Alternate Universe of 40K Astartes legions and discusses how the heresy would play out between them. Since then it has spiralled into a near-total overhaul of the 40K universe as a whole. Although there are variations in quality and completion, the project feature original art and write-ups for the new primarchs and their legions, original regiments of the Imperial Army, a new take on the Squat, and other warhammerania. For those interested in the origins of the project: Archived /tg/ threads can be found at http://archive.moe/tg/thread/34414189/ (Initial Legion creation) and http://suptg.thisisnotatrueending.com/archive/34432982/ (Alternate Heresy thread)
Imperium Asunder, AKA the /tg/ Heresy II: Electric Boogaloo
Yet another alternate Heresy with all-new Primarchs, only one where the Emperor is outright killed and Chaos consumes half the Galaxy, while the Loyalists fracture into a number of warring empires on the Eastern Fringe.
Warmasters Triumvirate, AKA the /tg/ Heresy III: Reloaded
A third alternate Heresy with new Primarchs. After the Emperor is incapacitated relatively early on, he leaves three of his sons in charge of the Great Crusade, the Warmasters Triumvirate. When more power is given to the Council of Terra and regular humans, tensions begin to rise. This one has 21 Space Marine legions, pitted against each other in a three way Brotherwar between the Imperial Loyalists, Chaos Traitors and Confederated Seperatists.
The Roboutian Heresy
The true heresy has begun: Papa Smurf takes the place of Horus and fucks over the Imperium. Much shedding of blood, sweat and tears ensues, with generous helpings of manliness on the side. It's pretty awesome.
Inspired by the above mentioned Dornian Heresy, circumstances happen that lead to the Primarchs who turned traitor in canon to stay loyal and the loyalists to turn traitor. For this Heresy's loyalists this ranges from having a small point that causes a major divergent in their lives, like Konrad and Angron, to having completely different lives like Lorgar. The Traitors all at a certain point have a moment that led them towards Chaos, some better done than others, even the fic's writer admits El'Jonhson's could have been done better, but the rest bring much tragedy and sorrow, except Vulkan who is this timeline's Nagash. Even then, Vulkan's moment of divergence is absolutely horrifying and the only reason it isn't sad is because how awful Vulkan is in this timeline. However, even Vulkan's horrors pale in comparison to that of Corvus Corax.
Can be read here (also contains sidestories and word of god).
Warhammer High
Technically an Alternate Heresy, as in there was no Heresy at all and the Emperor decided Malcador's ideas were not stupid after all and made 19 female Primarch children to give the Primarchs some responsibility Post-Great Crusade, something to live for, a chance for family, and because he really wanted Grandkids.
Imperium Ascendant
The Most Fuck-Ass Awesome Timeline: The Legion of the Damned are sent back in time by the Throne-Emperor to stop the scattering of the Primarchs by Argel Tal. After they succeed, the Emperor of the past looks upon the future that is the galaxy of 40K and vows to ensure that such a nightmare will not come to pass as the Ascendant Imperium strikes out against the darkness. Currently at Twenty Chapters with no sign of stopping.
Brotherhood of the Lost
Another one by Bolter & Chainsword, with the starting question being: "What if the canon legions were replaced by lost legion projects?" A three-way war between the loyalists, insurrectionists, and the smaller suzerainty, lasting for decades. Sub-forum can be found here, and a wiki here.
Nobledark Imperium
Probably one of the more divergent Alternate Heresies out there. Like Warhammer High technically an Alternate Heresy despite there not being a heresy at all. Nobledark is as much a retelling of the 40k universe with intentional twists as it is a straight alternate timeline, sort of like Hektor Heresy or Imperium Asunder, though in general all parties recieve a buff to reason and common sense, as you would expect from a universe that is nobledark as opposed to grimdark.
Instead of earning the ever-lasting hatred of the Chaos gods by doing {{REDACTED}} that led to the creation of the primarchs (who in this timeline are the Emperor's greatest, though otherwise similar to canon in name and deed), in this timeline the Emperor did so by plotting with Eldrad to create a last alliance of men and elves agreeing to a team-up between the nascent Imperium and the eldar to free Isha from Nurgle’s garden to weaken the Chaos Gods in exchange for access to the Webway and anti-Chaos lore.
The Imperium and eldar expect to go their separate ways after the Raid on Nurgle's Mansion, until Chaos decides to supercharge the War of the Beast in order to show those mortals what happens when you steal fire from the gods. The Chaos Gods don't manage to turn any primarch (though they get really close with Horus), the Emperor having told the primarchs what Chaos what it is and why it is important to not touch it beforehand. Humanity and eldar are forced into an alliance once again, resulting in an Aesir-Vanir-esque political marriage between the Emperor and Isha. Although things are bad with the biggest green tide the Imperium has ever seen and Luther convincing the majority of Dark Angels to go traitor, they only gets worse when the true mortal catspaws are revealed.
Because that buff to competence and common sense? Chaos gets it too. And in a spectacular display of long-term planning, instead of consuming ALL of the pleasure cult-worshipping eldar in the Eye upon their birth, Slaanesh only consumed MOST of them. So now in addition to daemons, orks, and traitors, you have an entire army of insane, Chaos-worshipping fair folk who just declared holy war on the Imperium and their heretic kin.
And it all kind of spirals out from there.
Can also be found at Nobledark Imperium Drafts, the other main page for the project.