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 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.
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, 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, the Iron Warriors remained siege masters, the Sons of Horus became the crusading Black Templars, 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, so Abaddon (takes over as leader 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 the Sisters of Battle never existed, because they were wiped out by the Word Bearers when they were still the Brides of the Emperor. Nicely done, Bolter & Chainsword. Your Spiritual Liege, Matt Ward, would be proud.
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
https://www.fanfiction.net/s/10578370/1/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 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.
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.