Some video games (from adventure games to dating sims) like to feature multiple endings as a way to increase replay value, by changing various elements and branches of the plot to reflect whatever choices the player made during the game.
This creates a problem when attempting to make a sequel (or adaptation) based on such a game: Which branch (and ending) of the plot gets to form the canon backstory of the new work? The production team must make a decision, and make one fast, declaring one to be the canon ending and cutting the other ones off. They're still canon in their original game, but not with regard to the new work.
In short, cutting off the branches is when one of the multiple possible endings in a game is considered the canon one in a future adaption.
Related to story branch favoritism: the plot branch that receives the most focus is more likely to be chosen as canon in a sequel. Contrast with third option adaptation, which ignores all the various plotlines and picks an outside choice. When the next work is also a video game instead of an extended universe entry, this can sometimes be averted with old save bonus or Schrodinger's question. If the branches were selected immediately from character selection, you're using Schrodinger's player character. See also canon name, where a character who didn't have a given name at all in the first game, is given one in the next. Merging the branches is a specific form of this where events from several mutually exclusive story branches are declared canon, rather than a single specific branch. See also no canon for the wicked, where the hero path is exclusively canon in a franchise with a morality system.
Averted with the original Resident Evil. During the events of the game, either Barry Burton survives and Albert Wesker sets off the mansion's self-destruct sequence (if you used Jill Valentine as your character), or Rebecca Chambers lives and Wesker's slaughtered by the Tyrant (if you used Chris Redfield instead). Future games show that both stories are canon: both Barry and Rebecca survived and Wesker was slaughtered by the Tyrant (so we can assume it was Chris who blew up the Tyrant). Interestingly, the storyline of the series wouldn't had been affected in any way if Rebecca was killed off, since her only other significant appearance was in a prequel. Barry is at least mentioned in Resident Evil 2 and makes a cameo in Resident Evil 3: Nemesis.
Resident Evil 2 has two story paths depending on the order in which the player plays through both protagonists' storylines. Resident Evil 6 follows the storyline from the Claire A/Leon B scenario.
Resident Evil 3 has three endings; one where Jill and Carlos escape after killing Nicolai, one where Jill and Carlos escape with Barry while Nicolai gets away, and one where Jill and Carlos escape with Barry while Nicolai is killed by Nemesis. Nicolai's escape is considered canon according to Word of God, even though many fans preferred that Nicolai's death occured to bring closure to the game.
Neverwinter Nights 2 and its two expansion packs allow for quite a few possibilities between them, but ultimately hints towards one set of events for the Knight-Captain. The main character canonically has to have gotten the good ending for the original campaign in order for references Ammon Jerro made in Mask of the Betrayer to make any sense; likewise, the presence of One of Many in Storms of Zehir and some of its allusions imply that the character then succumbed to the spirit eater and became evil, killing Okku and rampaging across Rasheman.
Knights of the Old Republic II allows the player to choose the gender and alignment of Revan from the first game. In either event, the changes are largely cosmetic, pretty much only affecting the gender Revan is referred to as and whether the Republic admiral appearing in certain cutscenes is Carth or not. It should be noted that, since both games are part of the Star Wars canon, only one ending for each game (light side male for the first, light side female for the second) is considered the version that "really" happened.
However, the second game has hints of Take a Third Option, as the canon scenario is light-side female, but with Handmaiden (who is only available to male PCs) as one of the Exile's companions. If the game had been finished, Handmaiden was supposed to have joined you if you were on the light side (then Visas Marr if you were on the dark side), meaning a female Exile could recruit Handmaiden.
School Days. The original game allows for Makoto to end up with one (or more) of several very different girls. Both the anime and manga adaptation, however, focus on the love triangle between Makoto, Kotonoha and Sekai, though they ultimately play out rather differently. The anime is an interesting case study — it's what happens when you're determined to avoid ruling out as many ending as you can. Makoto hooks up with every girl he can end up with in the game and more besides. Trouble is, this by definition makes him an utter jerkass, and more or less demands his eventual death.
Most sequels in Command & Conquer assume the good guys won the previous game. The fact that the Firestorm expansion for Tiberian Sun has a story where both sides win may be an attempt to correct that.
The third installment has no canon and non-canon storylines. Because, there's only one course of events depicted, with the players' faction choice merely determining which side they're viewing the events from. Many events that the Nod PC does are mentioned in the GDI campaign, and vice versa.
The original animation of Kanon leaves out large chunks of the Mai, Shiori and Makoto arcs, leaving them feeling rushed, contrived and confusing. The remake largely fixed this problem, even addressing the jilted haremettes' romantic advances toward the main character and having them get over it believably.
With three very different storylines that diverge early on, the Fate/stay night anime and manga both had to choose somebody. The default storyline (Fate) was the logical choice; fans of Archer and Sakura were inevitably going to be disappointed. Nonetheless, anime the producers gave those fans what they could, such as a Matou Zouken cameo, a magical outfit meant to suggest Dark Sakura, and Bait-and-Switch Credits where Shirou fights Archer. The manga also features elements from "Unlimited Blade Works" (such as Caster taking an earlier front seat as antagonist and Archer's open attempts to kill Shirou). In the end, though, fans of the "Unlimited Blade Works" scenario get the movie, and fans of "Heaven's Feel" get extra material in Fate/hollow ataraxia and lots of doujin works.
The Mega Man ZX series may be digging itself a hole of this sort. The first game has two possible player characters, Vent and Aile, whose stories are similar but irreconcilable. The second has two new player characters — one of whom coexists with Vent and the other with Aile. There is a manga based on Megaman ZX, and the main character they chose to follow is Vent.
The manga based on the Galaxy Angel video games not only rules out the ending for Forte, Vanilla and eventually Mint, it also throws out much of the Milfeulle, Ranpha, Chitose and Shiva stories, as well as the overarching story. New scenes were invented in their place, giving Shiva a bigger role, having a Love Triangle emerge between Milfeulle, Tact and one of the other girls (Ranpha in the first series, Chitose in the second) and turning Eonia into Schrödinger's Cat to facilitate a Gecko Ending.
The romance events in the game were fairly 2ndary plot-wise and did not change the main story much.
On the other hand, there has been a recent trend to avert this. Examples include the recent equivalents of both games listed above (the new Mortal Kombat has a "story mode" that tells a single, unified version of events through the eyes of a series of protagonists, while BlazBlue builds its entire premise around deconstructing this).
Blizzard's early WarCraft games were like this. In order to have a sequel worth mentioning, they decided that the Humans (the "good guys" of the first game) had been defeated and sent packing, as refugees, to nations on the northern half of the continent...and then, five years later, the Orcs (the "bad guys") decide to follow them, lusting for more conquest. In War Craft II, the Alliance victory is considered canonical, as is their "successful" campaign in its expansion, Beyond the Dark Portal. However, it should be noted that missions in both campaigns are considered canon. The only missions that aren't canon are the ones that end the campaign and don't allow for the canonical ending of the story. Blizzard mostly abandoned this method with StarCraft and all following Real-Time Strategy games, instead constructing the story so that one campaign flowed into the next... but StarCraft II: Wings of Liberty does have two missions where a player must make a decision about whether to help an ally or not. In both cases, the canonical storyline has you helping your ally—Ariel Hanson and Gabriel Tosh. A third mission, late in the game, requires a decision that affects how the final battle is fought, but is deliberately vague in terms of canonicity.
StarCraft II: Heart of the Swarm leaves the first vague, implies the second ended one way, and picks the third for why a mission in the same location has to be dealt with the way it is.
The Diablo series contains a minor example of this. The first game allows you to choose one of three characters to play, a male Warrior, a female Rogue, and a male Sorcerer. After defeating Diablo, this character embeds his soulstone into his or her forehead in an attempt to contain Diablo forever. It doesn't work, and in the sequel the hero is possessed by Diablo, becoming the game's villain. Although never explicitly stated, it is pretty clear that the Warrior is canonically the one who did so, as the character is male (unlike the rogue) and white (so not the sorcerer). If you look very carefully you can find hints about what happened to the Rogue and Sorcerer, but they clearly didn't do as well as their meat shield buddy, if "possessed by Satan" can be considering doing well. It is implied that the rogue and sorcerer go on to become minor bosses for earlier quests (Blood Raven and The Summoner respectively).
Diablo III mentions the role of "heroes" in the events of the second game, but The Book of Cain specifies that all five of the original character classes were involved in defeating Diablo the second time.
It was pretty obvious which ending of Drakengard was going to be used for the sequel. It was the only ending remotely considered good, but the Mind Screw ending leads to NieR.
At the end of Blood Omen: Legacy of Kain, the player has the option of making a Heroic Sacrifice for peace, or to rule over a broken land. Alas, peace doesn't make for good sequels... His choice turns the world into a blasted wasteland. And it was the better choice for the world in the long run. It's complicated.
Most of the Super Robot Wars games allow you to pick and choose between a variety of main character combinations (usually a male and female) and a choice between a Real Robot or a Super Robot (4/F/F Final being the first of the lot), but the games that plays this trope straight are the Alpha series. In Alpha, players have four different male and female portraits, with four distinct personalities to choose. This is resolved in Alpha 2...somewhat, by making one of the characters, Kusuha Mizuha (and Brooklyn "Bullet" Luckfield, by extension), become the canon protagonist of the Alpha series, by giving her a Super Robot route in Alpha 2, while adding three more routes: a male Super Robot route, and male and female Real Robot routes. In Alpha 3, Kusuha retains her Super Robot route, and three more routes are also made, with the added bonus of having the characters from Alpha 2 reappear in the Alpha 3 routes. Example: Cobray Gordon, the male Real Robot pilot of Alpha 3, has Arado Balanga, the male Real Robot pilot from Alpha 2, appear only in his route, with the other pilots following suit. All well and good, right? But then Sanger Zonvolt (the male Super Robot pilot in Alpha 2, who first appeared in Alpha Gaiden) appears in all 4 Alpha 3 routes, not just the Alpha 3 male Super Robot route.
Alpha also has a rather complex secret system and had to pick and choose which secrets were obtained and which weren't when going into the sequels. In Alpha 1, Zechs, Quess, Emma, Four and both Puru's were canonically recruited and appear in the sequels. Sara was not, nor was EVA 03 salvaged. The Macross series events happened (Milia became a miclone and piloted a Valkyrie. Necessery for Macross 7 in alpha 3), and Gunbuster acquired it's extra weapons. Dunbine secrets are irrelvant as Dunbine isn't in the rest of the series. Alpha Gaiden's secrets are also irrelevant as the series there don't appear elsewhere, except for future Sanger, who canonically wasn't recruited because everyone is weary of the present Sanger only remembering him as an enemy. In Alpha 2 Haman wasn't recuited and died so Zeon would be wiped out entirely to make way for Zaft in Alpha 3. Musashi died to better move the Getter plot, and Radora and Takeru weren't recruited (as only 2 characters could recruit them and it would complicate things) However Heinel and Richter survived and assisted the heroes against Gan Eden.
The Alpha 1 secrets are notable - it's actually impossible to get all of those secrets in a single run through the game, requiring a total of three or more to get them all. Also, Gunbuster DID get its Tomahawk and Home Run, but it also somehow LOST one of the secret attacks, the Buster Tomahawk Boomerang.
Fortunately, Banpresto handled this cleverly: in Alpha 2, Sanger's route begins with him waking up when the Earth Cradle is destroyed. In the Kusuha/Kusuha, Arado/Cobray, and Ibis/Selena routes, the Earth Cradle is never destroyed, thus Sanger has just woken up in Alpha 3, whereas in Touma Kanou's route, which follows Sanger's Alpha 2 route, EVERYONE has met him before from Alpha 2, and he has a lot more experience in piloting the DyGenGuar.
SRW Z meanwhile avoided this problem by only have the protagonist characters reappear in Z2, without supporting ones, let alone secret characters although it was also mentioned Four Stella and Rey are still alive. It avoids protangoist choice problems by having both Rand and Setsuko appear in Z2 and be vague as to which one actually was with Zeuth in Z1.
However, if we assume that SRW Z Special Disc is canon, then both Setsuko and Rand were part of ZEUTH. This doesn't really conflict too much with canon, since the Setsuko Route and Rand Route were already known to take place at the same time.
Z2 seems to act as if BOTH characters were part of Zeuth. Which is impossible according to Z1. The one not selected is an enemy turned NPC assisting from behind the scenes and doesn't awaken their sphere, nor get their partners back. Not only that but their early route events happen without them as Xabungle/Turn-A/Gainer people don't know Rand and Zaft/Zeta/Gravion people don't know Setsuko if they aren't the main. The only thing that always happens is both their early encounters with Asakim (where he helps Rand and kills Setsuko's allies) but even then it's not quite the same as Mail isn't located when Rand shows as an enemy (where as she would be in his route) while Toby is already dead when Setsuko appears as an enemy (in her route he'd only be just about to die). In Z2 both Rand and Setsuko appear with their fully awakened spheres and upgrades, Mail is with Rand and the Glory Star are mentioned to be back in Zeuth world. And both of them have the same friendships they developed in their story route (Rand is buddies with Gain, and Roger, while Setsuko is buddies with Kamille and Shinn) which again shouldn't be possible if one of them is still mostly a stranger to Zeuth.
The Original Generation series also tends to run into this when characters and storylines from the various games in the franchise appear. Sometimes, Banpresto chooses one over the other, but more often, they Take a Third Option:
OG1 retains Kusuha and Bullet's Alpha portraits and personalities, but used the other six of the eight possible Alpha protagonists by means of Divergent Character Evolution. Kusuha and Bullet are placed in their Super Robot Alpha roles (as a foreshadowing of their Alpha story in OG), while another pair (Ryoto Hikawa and Rio Mei Long) are given the Real Robot Alpha route (which originally negates the Super Robot example in Alpha, concerning the fate of the Choukijin). The third pair (Tasuku Shinguji and Leona Garstein) are given all-new original robots never seen in SRW before, with the fourth and final pair (Yuuki Jaggar and Ricarla Borgnine) being introduced in OG2 using existing robots from Super Robot Wars Advance. OG1 itself possessed a very minor example: the choice to play as either Ryusei Date or Kyosuke Nanbu as the protagonist. The first halves of each story are completely separate, but canonical to each other. The second half is shared, with a few slight differences. Unfortunately, when OG2 is released, the second game carries on with Ryusei's version of the second half, making Kyosuke's OG1 latter half Canon Discontinuity.
In Advance, the player has a choice of Lamia Loveless or Axel Almer. Whoever the player doesn't choose becomes The Rival throughout the game, minus whatever quirk they suffer when chosen (Speech Impediment for Lamia, Laser-Guided Amnesia for Axel). In OG2, Lamia's chosen and much demand for the return of an amnesiac Axel ensued, due to a massive Flanderization of Axel by turning him into a much bigger Jerkass than he was in Lamia's Advance route. The Enhanced Remake of OG2 not only lightens his character considerably, forcing him into a Noble Demon status, but come OG Gaiden, he pulls a stunning Heel-Face Turn to the delight of fans. Then Endless Frontier EXCEED finishes the job, with Axel getting the Amnesia and taking up the personality he gets in Advance.
Colony Wars was a Space Sim that had 5 possible endings, the best being one where The Empire was thoroughly defeated by La Résistance and peace was made throughout the 5 systems, too bad that doesn't make for a good sequel. So instead, the canonical ending was the ending where La Résistance beat The Empire back to the solar system but were unable to take Earth and instead had to settle on destroying the only star gate our of the system so that the Empire was trapped in the Solar System with scarce resources until they could build a new star gate generations later.
Originally, The Secret of Monkey Island had two slightly different end paths, neither of which had a practical effect on the actual endgame: Either you sail back home from Monkey Island with your ship and crew, or you "accidentally" sink their ship and ride home with Herman Toothrot, the local hermit. Even though sinking your ship was an obscure action to begin with, that ending was made canon in the fourth game in the series, where Guybrush's former crewmates, now back home on Méleč island, go out of their way to avoid him because he left them stranded on Monkey Island.
More subtly, dialogue choices in the first and second game make it possible to play Guybrush as a either a Genre SavvyDeadpan Snarker or a lovable Genius Ditz, but the third game in the series prefers the latter characterization.
This is probably because it saved Dominic Armato having to read as many lines. It's also implied that Guybrush being with Elaine had mellowed him out somewhat (or, more likely, stopped him from doing sociopathic behavior because she would lecture him about it if he did).
The anime based on Star Ocean: The Second Story, Star Ocean EX, merged pretty much all the story of the first part of the game, changing it to make it all possible to happen together. For instance, they just encounter and recruit Ashton, instead of having to backtrack or miss him. Later on they meet Opera and Ernest, which doesn't happen if you recruit Ashton. The gaiden sequel, plus the third main game's manual confirm that every possible party member was canonically recruited.
Tales of Symphonia brought Relationship Values to the series. It also made it into the Massive Multiplayer Crossover tactical-RPG Tales of the World: Narikiri Dungeon 3, which lets the player set up custom parties of Tales series characters and awards parties bonus titles for certain team-ups. One of these titles is "Love-Love?", which goes to canon couples, such as Cless/Mint and Chester/Arche from Tales of Phantasia, Rid/Farah and Keele/Meredy from Tales of Eternia, and Lloyd/Colette from Tales of Symphonia. Ironically, the sequel actually allows you to avert this particular cone, with an optional cutscene that the player can choose to follow whichever relationship choice they want.
The sequel to Symphonia also averts this by letting the player choose which relationship was "canon" in the previous game, in a bonus cutscene — with one exception playing the trope straight: the Kratos alternate storyline for Symphonia cannot be made canon in Dot NW since Zelos is alive in the sequel, and choosing Kratos in Symphonia required to kill him.
Supreme Commander's expansion Forged Alliance doesn't explain which ending is actually canon, but simply, after a little expositionary cut scene, dumps the player directly into "1 year later", as the Big Bad overruns the galaxy. It can be deduced it's the Aeon one, because the other sides were wiped out in the UEF ending and space travel was prevented for years in the Cybran one. However, it is implied that whichever side you choose you are the same commander as you would have been in the first game for that faction.
In one mission of Mechwarrior 4, Ian Dresari, you, can either save your sister Joanna or secure a cache of weapons for the war effort. The game ends with either Joanna or Ian ascending the throne as Duchess or Duke. The Black Knight expansion pack assumes that no only did Ian fail to save his sister, but is now ruling as a tyrannical despot.
The Muv-Luv games not only have multiple story paths for Extra and Unlimited, but multiple universes and Groundhog Day loops too. The final game, Alternative, has a linear plot that explicitly references multiple paths from the previous games.
Mass Effect 2 goes with the Old Save Bonus approach. Unfortunately, if you don't have a save to import, the game gives you default choices that are not only mostly Renegade such as killing the Rachni and the Council, but also some of the worst ones that very few players ever choose, such as killing Wrex on Virmire and electing Udina to the council. Some fans speculate this is a sneaky way of encouraging players to play the first game instead of jumping into the sequel blind. The PlayStation 3 version, due to the fact that the first game wasn't initially released for that system, includes an interactive comic book that allows the players to make decisions about major events. This feature was later released as DLC for the Xbox 360 and PC versions.
Mass Effect 3 requires that Shepard survived the suicide mission of Mass Effect 2 (you can't import a save game where Shepard died). This should be fairly obvious, as BioWare said when the second game was released that the trilogy is less about the universe and more about Shepard's story and how it affects the galaxy. The Stinger of the third game drives the point home.
The spin-off novel Retribution cuts off the branches for players who appointed Anderson to the Council, and in Mass Effect 3, Udina is the human councilor no matter what (if Anderson was on the Council, he resigns between the games). Also, the Council in 3 is always either the original one from Mass Effect 1, or a new, but still mixed-species one. There is no all-human Council, even for playthroughs in which Udina proposed making one at the end of the first game.
Done to a depressing extreme in Baldur's Gate II. The game dialogue and set-up tells you exactly who you travelled with by the end of the first game (Khalid, Jaheira, Minsc, Dynaheir and Imoen) and tells you exactly how you behaved (heroically). Needless to say, rationalizing what you are shown and told in the intro level was very difficult if you're getting the Old Save Bonus from a Chaotic EvilPriest of Talos.
While left somewhat unclear, Overlord II suggests that the previous Evil Overlord was something of a Noble Demon who at the very least saved the Elves from extinction. The game also goes on to say that Rose was the canonical choice for Mistress.
It may just be retconning the decisions needing to be made; you can have multiple mistresses in the sequel, and in the event where you choose to save the elves or steal the gold you can easily have enough minions to do both (the game goes with whichever is finished first).
The second Mana Khemia game hints that the canon ending from the first game was Flay becoming a criminal mastermind and Vayne playing hero.
Strangely, it also implies that the canon ending was Pamela being freed from the school and traveling with Vayne, as she does not appear or get referenced to in the entire sequel, and she would still be at Al Revis under any other ending.
Fallout 2 avoids many specifics by taking place in the area just north of the one where Fallout 1 did, and the Vault Dweller's diary that serves as the intro story to the Fallout 2 manual is somewhat vague at certain key plot points (i.e. whether you sided with Killian or Gizmo, saved Necropolis, or shot the overseer), but from what you do learn it seems that canonically the Vault Dweller was a generally heroic figure (i.e. saving Tandi and Shady Sands, which would eventually become the New California Republic). The diary also mentions that party members Dogmeat and Ian died during the course of the adventure, although this is quite likely Lampshade Hanging of first game's sub-par companion A.I. - Dogmeat specifically is mentioned to be incinerated by a force field in the Mariposa military base, which is guaranteed to happen assuming you have him at the party by then and can't pass numerous skill checks to disable the fields for good. Finally, from the appearance of the massive statue of the Vault Dweller in the NCR square, it seems that the vault dweller was male.
Similarly, Fallout: New Vegas avoids references to Fallout 3 by setting it on the other side of the country. New Vegas does have a few references to events in Fallout 2, however: The Chosen One helped Vault 15 integrate with the NCR (hence why they're expanding into Arizona) and left Tandi alive. References to a very wasteland-accustomed "Mr. Bishop" also implies that The Chosen One was male and slept with one of the Bishops, but the ending that usually comes from that scenario is averted since the Wright family is apparently in control of New Reno, having out-competed the Mordinos and Salvatores. One thing that is confirmed about Fallout 3's story is that Moira Brown completed the "Wasteland Survival Guide" with a fair amount of success, since it's available as an item that boosts the Survival skill in New Vegas.
The original Metal Gear Solid has two endings; a "good" one where Meryl lives and a "bad" one where Snake finds her dead. Metal Gear Solid 2 doesn't mention Meryl, but Snake is wearing his bandana of unlimited ammo, a gift he got from Meryl in the "good" ending. While the book "In The Shadow of Shadow Moses" (Nastasha's account of the events in the previous game from her perspective) suggests Meryl survived, the book "The Shocking Conspiracy Behind Shadow Moses" explains the main character found the bandanna on the beach and Snake took it from him (implying Meryl was never there to find it). Being deliberately confusing was one of Metal Gear Solid 2's main themes. Not being deliberately confusing was one of Metal Gear Solid 4`s, which had Meryl return in an awkward-ex-girlfriend role.
What makes it even more confusing (and possibly an aversion of this trope) is that later games imply that Otacon and Snake left Shadow Moses together, something that only happened in the ending where Meryl died. Of course, considering that the entire franchise has No Fourth Wall, it's entirely possible that both endings are somehow canon (because you, the player, probably played through the game at least twice for both of the endings, then clearly Snake has as well).
Fire Emblem: Thracia 776, the midquel to Geneaology of the Holy War canonizes Levin/Fury, whereas in the first game you could choose between her and two other girls. (Well, technically six other girls but since only Fury, Sylvia and Tiltyu's sons can use Holsety there's no point in the other four.)
On the other hand, they averted this with Raquesis by implying BOTH her predistined pairings were canon. (i.e. Nanna's father is Finn and Delmud's father is Beowulf)
Fire Emblem Awakening has another aversion. The DLC battles involving the characters from Fire Emblem Akaneia make vague references to New Mystery's player-created character, and canonise their name asKris, but what pronoun is used to refer to them depends on the gender of Awakening's Avatar, meaning male and female Kris are both equally canon.
The only ending of Silent Hill Origins that is canon is the Good Ending, a necessity since it's a prequel.
The flash game Imaginary Realm has multiple endings which depend on how well you do in the cooking minigame. The canon ending is the worst possible one you can get, which you "earn" by cooking any of Rosey's recipes.
If you don't import your Warden from Origins to Awakening, you have to play as an original Orlesian Warden-Commander and the expansion automatically sets certain story flags, such as Alistair being King of Ferelden.
Dragon Age II offers not one but three possible pre-built histories comprising of both Origins and Awakening story flags if you don't import an older save file. If you import just the Origins save without Awakening flags, those will be preset for you.
Dragon Age: Inquisition will offer only one pre-built history if you don't import an old save (i.e. Martyr + Mage!Hawke sides with mages), but the Dragon Age Keep online service will allow players to modify it as they see fit, effectively giving them the power to cut or grow the branches they want.
Then, there is the matter of the so-called "BioWare canon", a unified timeline where all official non-interactive installments set after Origins take place. According to the Word of God, these are meant to be read with a disclaimer "If these events contradict your game canon, then they never happened in it (or maybe something similar happened)":
Asunder, a novel bridging parts two and three, establish that First Enchanter Irving is alive in BW canon, Shale was canonically freed and has discovered her origins, and both Wynne and Shale have been taken to fight the Archdemon. This, in turn, implies that the Warden did not defile the Sacred Ashes, otherwise s/he would have to kill Wynne.
According to The Silent Grove miniseries and its sequels, Alistair is King, though it's unclear if he's married to the Warden, Anora, or ruling alone. Isabela made it to the end of II, instead of leaving or coming back only to be sold out to the Arishok. Speaking of whom, he's dead and Sten (alive and returned home) has taken his position.
Being an online series, Red vs. Blue : The Bloodgulch Chronicles was able to be a rare non-video game example of this trope. The final episode had three different endings (four more were added in the DVD). When the series continued into Reconstruction, one of them was deemed canon. However, it was obvious which one was the real ending because none of the other 6 endings would work in a sequel. In 4 of them, everybody dies and the other two reveal the series to have been All Just a Dream (while also killing off either Grif or the entire Blue team respectively).
All Chrono Cross says about its predecessor Chrono Trigger is that all of the main characters died in various horrible ways. Also, the game has at least ten endings, and the one that's considered canon wasn't actually put in the game until the Updated Re-release for the PlayStation. In that ending, Dalton takes over Guardia, and the heroes set up the long chain of events that leads into Cross.
The film Clue is a rare example of this being done for an adaptation of a board game. They don't cover all the possible killers - and, in fact, one of the endings is utterly impossible to achieve within the game - but the multiple endings get the basic point across.
In the original Final Fight, any of the three heroes (Guy, Cody, or Haggar) could throw Belger off his building at the end of the game. In Final Fight 2, it is Cody who is shown delivering the finishing blow to Belger in the opening intro and this actually becomes an important plot point in Final Fight: Streetwise (in which Father Bella is seeking revenge on Cody for killing Belger).
Gothic handles the choices of the previous game by having almost everyone that would care dead (or outside the area in Gothic 3's case), or only talking about events common to all three paths. There are however a few dialogs that reference specific minor choices. One early conversation in Gothic 2 establishes that The Nameless Hero did not pay Bloodwyn protection money (as he will reference the consequence of not doing so). One interesting bit in the expansion for 2 suggests he killed Bloodwyn (never required or recommended, but deserved), which occurs during a conversation with Bloodwyn (he notes he survived).
In RuneScape, the "Temple of Ikov" quest has you choose whether to protect the Staff of Armadyl or steal it and give it to the bad guy. When the developers made the sequel quest, "While Guthix Sleeps", they realized the plot sort of hinged on the bad guy having the staff, so everyone who chose to protect it received a note from the guardians that it had been stolen by somebody else.
Shin Megami Tensei I had three endings. The sequel takes place under the premise of the Neutral ending having occurred.
In Persona 4, acquiring the Ultimate Persona for the members of the Investigation Team is optional, and Updated Re-releasePersona 4: Golden gives the party brand new third-tier Persona; subsequently, Arena features the Investigation Team with their default Persona.
Despite Persona 4 having four different endings, the game renders all but the True Ending non-canon.
The Protagonists in Persona 3 & Persona 4 are able to date a number of different girls over the course of the game; Arena makes no reference to any of the possible pairings.
Persona 3 Portable added an optional female protagonist in place of the male protagonist in the initial game; Arena explicitly refers to the male protagonist.
Left 4 Dead has the campaign "The Sacrifice", which ends with one of the original Survivors dying in a Heroic Sacrifice to allow the others to get to safety. In the game, any of the four characters can make the sacrifice, but the tie-in comic and the sequel campaign "The Passing" shows that Bill is officially the one.
Notably, "The Passing" came out a full year before "The Sacrifice", making Bill's death a foregone conclusion. All the more egregious as the only reason why he's dead in the former is due to his voice actor being unavailable during its production.
SHUFFLE! has an interesting subversion to this trope. Nerine got the first canon ending with the sequel Tick! Tack!. Then Asa got the canon ending in the anime. Lisianthus got the canon ending in the manga. And finally Kaede got the canon ending in Really? Really! which ignores the events in Tick! Tack! Poor Primula has so far been left out as have all the other sub-heroines that get full routes in later games.
Inazuma Eleven 2's One Game for the Price of Two gimmick only had the typical differences between the two versions (different rival teams, optional sidequests, Optional Party Members, etc.), so this was pretty easy for the anime adaptation to deal with. Then Inazuma Eleven 3 had actual story differences between its versions, although they were still mostly reconcilable, so the anime had the events of both versions occur with a bit of effortnote For example, at one point in the anime, the cast split up into two sub-teams and ran off in opposite directions so that they could be two places at once. This conveniently happened right after 6 of the rivals-turned-Optional Party Members joined up, which allowed them to have the requisite headcount of 11 people on each sub-team to participate in the ensuing soccer matches.. However, now it's been recently announced that the fourth game, Inazuma Eleven GO, will have two versions but with gigantic differences in the story, even different Official Couples. So far, it looks like the anime's following the Shine version.
Early the First Edition Advanced Dungeons & Dragons adventure I6: Ravenloft (inspiration for the Ravenloft setting), there's a fortune-telling scene which DMs and players are encouraged to act out with real cards. Depending on the results, the Big Bad may have any of four different evil schemes, and the MacGuffin and information which the heroes are looking for may be in any of four different places. A similar gimmick based on a prophetic hypnosis session was incorporated into the sequel, Ravenloft 2: House on Gryphon Hill. When Ravenloft was reinvented as a full-fledged game setting, its designers Cut Off Branches that would have left the Big Bad destroyed or banished from his castle, while averting this trope in other respects by never stating precisely what the heroes of those adventures had encountered.
Sampaguita, the third game of the Visual Novel series Yarudora, boasts three Good Endings, five Normal Endings, and twenty Bad Endings; so, when a Trading Card Collection set was made and released, Good End 2 was chosen as the main storyline, while Good End 3, Normal End 2, Bad End 1, and Bad End 9 became Parallel Stories (and the remaining Endings not used at all).
Touhou: Later events have confirmed that the heroine of Embodiment of Scarlet Devil was Reimu, as well as strongly implying that the Scarlet Team went through Imperishable Night. Additionally, there's certain endings that obviously didn't happen, what with Kanako not being the god of the Hakurei Shrine, and the Palanquin Ship not touring Gensoukyou.
Kaleidoscope Dating Sim 2 is a rare example in which the joke ending of the original game is made canon. You see, the joke ending of Kaleidoscope Dating Sim 1 featured the male protagonist Cero turning into a mushroomfrom eating too many mushrooms in the forest, and in the second game the female protagonist Soffie has a chance of finding a talking mushroom while gathering mushrooms in the same forest...
Winter Assault presumably ended in an Eldar victory, given how Dark Crusade mentions that the Eldar betrayed the IG and Gorgutz both survived and killed Crull.
Dark Crusade's endings were pruned by Dawn of War II (and its novelizations) mentioning that the Blood Ravens beat, at the very least, the Necrons, the Chaos Marines, the Imperial Guard, and as of Retribution, definitely the Eldar.
Soulstorm didn't confirm a victor (probably because it was the Sisters of Battle, one of the least-popular 'good human' races, to say nothing of how unpopular Soulstorm itself was), but it did confirm that the Blood Ravens lost horribly.
Surprisingly, after Winter Assault, Gorgutz managed to avert this with each of his appearances, with a cutscene showing him deliberately escaping the conflict if he's defeated. This opens him up to appearing in any sequel should he be needed, and he's fairly popular.
Chaos Rising was confirmed by Retribution that Avitus was the traitor through process of elimination: the traitor had to have fought on Kronus (rules out Thaddeus and the Force Commander), while Tarkus, Cyrus and Martellus appear as playable characters.
An odd case was the return of Eliphas the Inheritor. Not only does the Dawn of War II game invalidate his existence, but he somehow switched sides for unknown reasons.
Retribution ended, predictably enough, with a Blood Ravens victory, which is confirmed in Warhammer 40,000: Space Marine when Titus encounters a handful of Blood Ravens marines who reference the "Aurelia Campaign".
The Code Geass RPG for the Nintendo DS is an interesting example; the "One True Path" is the anime canon, which you're forced to follow on your first playthrough. The New Game+ allows one to explore better (or worse) paths, all of which involve Original Generation villains Castor and Pollux. Interestingly, from the fourth playthrough onward, you can force yourself back onto the plot railroad by performing a certain action during a sequence where you control Castor that gets him killed and reasserts the anime plotline.
Fable II dodges this by occurring centuries after the original Fable and when during the rare moments when Fable 2's predecessor is mentioned having contradictory accounts as to what specifically occurred. Theresa's survival is about as close to canon as they get about it, and even then it's never specifically stated that the old blind seer of the second and third games is actually the Hero of Oakvale's sister from Fable either.Fable III occurs mere decades after Fable II, makes use of the Old Save Bonus method but only uses that to mention the Hero of Bowerstone's gender, and like II also rarely mentions the Hero of Bowerstone and is very vague as to what kind of person he/she was. However, the Hero of Bowerstone did end up becoming King/Queen, meaning that s/he ended up buying up all the real estate in the game.
The second installment of the Axis Powers Hetalia fan game Project NA gives four possible endings (True, Bad, Blah, and Treasure). While the third and final installment has not yet been released, Word of God says that the True ending where Matthew remembers his name as Canada and figures out how to use his powers with Alfred is naturally the ending the sequel will follow.
The original Wario Land ended with Wario asking a genie for a castle. Depending on how many coins the player collected, he ends up with anything from a birdhouse to an entire planet. According to Wario Land II and Wario World, he canonically got a large castle.
Clock Tower uses this between the first and second games; during the S Ending, it was possible to have Ann or Laura survive, but the sequel confirms that Jennifer was the Sole Survivor - meaning they join Lotte in the Doomed by Canon club.
In Borderlands 2, it is stated that Mordecai was the canonical champion of the Mad Moxxi's Underdome Riot DLC of the first game.
STALKER: Shadow of Chernobyl has not one, not two, but five possible endings. Two of them are secret, only one ending is good to any real degree, and it still leaves things ambiguous as to whether you did the right thing. The "good" ending is the one that is picked up in Call of Pripyat, at which point you find out that yeah, things got worse somehow.