Canon is any information that is considered to be "real", "official", or "true" in a fictional universe. For the most part, it is trivial to understand what constitutes as canon and what doesn't, as one needs to simply follow the storyline of a main Pikmin game. But there are some aspects outside of the Story Modes that could count as either canon or not.
Pure canon is all information that is undoubtedly canon; events that "really happened" in the Pikmin universe. This is mostly decided by the parties that develop the games and media related to the Pikmin franchise, meaning Nintendo EAD and Shigeru Miyamoto.
Currently, the main Pikmin games – Pikmin, Pikmin 2 and Pikmin 3 – are considered canon. Hey! Pikmin is a spin-off game due to being a different genre and using some different mechanics from the main games but since the story doesn't contradict the other games besides some inconsistencies, Hey! Pikmin is generally considered canon. Anything that happens within the Story Mode of each main Pikmin game is canonical. Bonus content, such as the reward obtained by completing all Pikmin 2 Challenge Mode levels with a pink flower, can vary in canon, but whenever it does not contradict with – and makes sense within the context of – the main Story Mode, it is considered canon.
Some content in some games could be considered canon or not. This could be because there is not enough information to accept or reject it as "real", or could simply be a matter of opinion.
Trophies, stickers, and other side-content in the Super Smash Bros. series features canonical information from elements in some franchises, and occasionally, adds its own information as well. For the most part, this extra information is created and approved by Nintendo, but is never confirmed to be true or false. This, combined with the fact that the information is contained from within a non-canon media, makes the canonical value of the information questionable. In addition, there are times where the likes of trophy descriptions contain information that directly contradicts the canon in the games and are as such, considered non-canon. For a list of such cases, see Mistake.
Some external content like the e-cards or the Pikmin Short Movies have information that matches up with the existing canon and makes sense in the Pikmin universe. However, no official word has been given on their canon, and because they do not belong to the main Pikmin series of games, their content is left as ambiguously canonical.
The amiibo compatibility in Hey! Pikmin is generally considered canon, assuming that Nintendo is believed to have existed inside the Pikmin universe. However, the Olimar and Pikmin amiibo existing in the game world sprout some paradoxes and overall doesn't make sense, so it's unlikely this feature is actually canon.
Pikmin 3 Deluxe's Side Stories mode gives Olimar's perspective before, during, and after the events of Pikmin 3's canon Story Mode. While Olimar's Comeback can be assumed canon (as long as an ending where Louie is not left behind is achieved), Olimar's Assignment is where the objectivity comes in, as for it to make complete sense it would have to take place during the Story Mode. While the events line up with what's said in Olimar's data files from the Story Mode, the locations in Side Story missions are drastically different from the Story Mode versions, much like in Mission Mode. So while the story events in Side Stories could be considered canonical to the main story, the map alterations, signposts blocking off locations, and possibly the use of SPEROs are likely non-canon.
Prima Games has a vague relationship with the developers of games they make guides for. On top of containing walkthroughs and tips, some guides include some extra information about aspects of a franchise; in the Pikmin series' case, this could be extra descriptions of enemies, for instance. Prima Games works with all sorts of companies, making it doubtful that they can have a meaningful connection with all of them such that the extra information they write can be accepted as canon by the developers. On the other hand, it is clear that Prima Games has a strong connection with at least some departments of the development teams, seeing that their guides usually contain maps and charts that were rendered using 3D models or in-game images, resources that can only be obtained legally by agreement with the developer company. The guides are also officially licensed by Nintendo. That said, the extra information presented in some guides is not backed up by the canon game at all, and some other information can be dubious, or even outright wrong, like the time requirements for all of the Defeat Bosses! missions, or the wrong scientific name for the Breadbug. With all of this in mind, it is not clear if the information inside Prima Guides can be considered canon or not.
Some aspects in the games are not canon whatsoever. They belong to the game, but are considered to "not have happened" in the Pikmin universe.
The Super Smash Bros. series feature games that are considered non-canon for the franchises that take place in them. This is clear due to the fact that, naturally, Pikmin does not share a universe with the likes of Mario or The Legend of Zelda. Pikmin Adventure, despite being directly related to the Pikmin franchise, is not canon. It does not, in any way, relate to PNF-404 or the actual Pikmin, but rather, it is a mini-game in Nintendo Land, themed around the Pikmin franchise.
Activities that happen on an alternative game mode in a Pikmin game are not considered canon. Said game modes were created for the purpose of entertaining the player, and for the most part, they do not follow the main Story Mode's canon. For instance, it is canon that Captain Olimar landed on PNF-404 and had to gather his missing ship parts, not that he chose to begin a challenge where he had to cultivate the most Pikmin possible in one day.
Unused content, prerelease information, mistakes and glitches are not canon. They are content that the game developers did not intend to provide to the players in a finalized game, and should not count as such for the purpose of deciding the canon.
Some media, like movies, have a specifically defined canon, in which what happens in the movie is objective truth in the movie's universe, and cannot be altered. Games, however, vary according to each player's experience, so some aspects of the gameplay cannot be correctly considered canon or non-canon.
For instance, it is no truer that "Captain Olimar first recovered the UV Lamp and then the Massage Machine" as it is the other way around. For this, common sense dictates that varying truths are not accounted for in the lore. Following the previous example, it is canon that Captain Olimar recovered his ship parts, but their order of collection is not confirmed. There are times where such events are confirmed in a different game, however, normally in the form of a leader outright saying it (e.g. in his notes in Pikmin 2). Naturally, this does not change what a player might have actually done in their playthrough, but it does define the "standard", canon-wise.
The ending obtained in a game is also not relevant to the decision of the canon. Rather, the events that unfold in a following game decide which ending is the canon one.
Overview of the canon
While on an interstellar vacation, Captain Olimar switches his ship, the S.S. Dolphin, to autopilot and stands up from the control seat to make a cup of tea. He fails to notice a meteor, which hits the S.S. Dolphin and sends it plummeting to the surface of a nearby planet. During the chaos, Olimar was thrown against the control panel, and blacked out. He awakens on the surface of the planet, and discovers that 30 of the Dolphin's ship parts were scattered around the planet. Olimar's space suit's sensors then indicate that the atmosphere of the planet contains oxygen, which is extremely poisonous to Hocotatians. Fortunately, the life-support system built into his suit was unharmed, but the remaining battery power would only last him for 30 days. After exploring the area, Olimar finds a dormant Onion. When Olimar approaches the Onion, it seems to awaken, and spits out a seed. Olimar plucks the seed, discovers Red Pikmin, and utilizes their abilities to get back the Main Engine, which allows him to pilot the S.S. Dolphin once again. During his expedition on the planet, Olimar comes across Yellow Pikmin and Blue Pikmin, in that order. He finally manages to retrieve all of his missing ship parts, and grabs a "shiny alien platter" as a souvenir for his kid, before blasting off back to Hocotate.
It is not known which ending is the canon one, but it could be considered to be the one where he gathers all ship parts, given that in Pikmin 2, Olimar has brought a souvenir home for his son, something that only likely happened after the collection of the Secret Safe, which is even implied by Olimar himself. In addition, it's revealed that Olimar's wife eventually finds a "secret cash stash", which can be assumed to be the Secret Safe. The ship's appearance in Pikmin 2 also supports this, as the antenna on the top of the Dolphin isn't bent and the lights on the sides are purple, which is only possible if Olimar collected the Secret Safe. The manual for Pikmin 2 also confirms that Captain Olimar did succeed in completely repairing the S.S. Dolphin.
When Olimar returns to Hocotate, he finds that his company had to take out a loan to repay the loss of a cargo of golden Pikpik brand carrots. Louie reported that a ravenous space bunny ate the shipment, but they were actually eaten by Louie himself, as he couldn't suppress his powerful hunger. The President explains their situation to Olimar, who learns that the S.S. Dolphin was sold to help repay the loan. The remaining loan is revealed to be 10,100 Pokos and, in shock, Olimar accidentally drops the "alien platter" souvenir on the ground. As the souvenir rolled into Louie, the Hocotate ship was able to suck it up. It analyzed the piece of treasure to be worth 100 Pokos, which lowered the remaining loan to 10,000 Pokos. As a result, the President sends Olimar and Louie back to the planet to collect more treasure in hopes of paying off their debt.
While landing, they fly through a small blizzard in the Valley of Repose, and try to maneuver through some tree branches. Unfortunately, Olimar hits one of the branches, and Louie falls out of his cockpit, into the snow below. The Hocotate ship barely manages to land, and ejects Olimar out of his cockpit. He gets up and rediscovers Red Pikmin. After a while, the duo are able to reunite and salvage a piece of treasure. During their search for treasure the following days, Olimar and crew discover Purple Pikmin and White Pikmin, and rediscover Yellow Pikmin and Blue Pikmin, in that order. Eventually, they collect enough treasure to repay the debt and return to Hocotate, but during the trip back to their home planet, Louie gets left behind. Olimar then returns to the strange planet with the President, and they recover Louie from the Titan Dweevil. After collecting the rest of the treasure on the planet, they finally go back to Hocotate.
Some time after this, the planet of Koppai is in the midst of a planet-wide food crisis. They decide to send unmanned scout vessels, called SPEROs, out into space to search for planets that contain edible matter. The final SPERO returns with data indicating that one planet has "unlimited food resources". Koppai names the mysterious planet "PNF-404", and proceeds to send three explorers to PNF-404 in search of food. Unbeknownst to them however, Olimar and Louie also return to the planet to collect more treasure, as Hocotate Freight's new business venture failed miserably and the company has fallen into debt once again. Olimar and Louie start their search for treasure in Flower Garden. The next day they go to Inside Forest, but at the same time, the Koppaites' ship, the S.S. Drake, mysteriously fails, ejecting the Koppaites into different areas. Captain Charlie wakes up in the Distant Tundra, finds Yellow Pikmin, and eventually loses them when he's confronted with the Vehemoth Phosbat. Alph then wakes up to find himself in the Tropical Wilds, encounters Red Pikmin, and reunites with the S.S. Drake. He then learns that they cannot return to their home planet without the cosmic-drive key, which is nowhere to be found on the S.S. Drake. On the same day, during the start of Olimar and Louie's expedition in Inside Forest, the two come across the cosmic-drive key, which Olimar takes as a souvenir for his son.
Olimar and Louie head to River, and Olimar realizes that a number of his logs and notes have gone missing. Olimar also buries the Scorch Guard here, along with a log, as he states that he doesn't need it anymore. Meanwhile, Alph makes his way to the Garden of Hope, where he gets Rock Pikmin and reunites with Brittany. Before they begin their expedition in Tundra, Olimar finds Charlie's impact site and leaves the Anti-Electrifier with a note, due to the area having "many electrical contraptions". After defeating the Armored Mawdad, the Koppaites make their way to the Distant Tundra, Brittany gets knocked off the ship and lands in a cave where she discovers Yellow Pikmin. (Although it is possible to achieve in-game, the Koppaites did not go to the Distant Tundra on day 3, as they would've seen the Hocotatians, which obviously didn't happen.) Olimar and Louie finally collect enough treasure to repay the second debt, but Olimar picks up a reading of a golden object in the Oak. He ignores Louie's warnings about the area, and they go to the Oak the next day. While Olimar records his log, he gets captured by the Plasm Wraith, and Louie runs away. Olimar attempts to escape the area several times, but the Plasm Wraith repeatedly knocks him unconscious, since his spacesuit puts him in forced-sleep. During his escape, Louie is somehow ejected into Twilight River while the ship itself crash-lands in the Quaggled Mireclops' arena, losing several of its parts in the process.
Meanwhile, Alph and Brittany reunite once more in the Distant Tundra, take down the Vehemoth Phosbat, and rescue Charlie. They then head off to Twilight River to pursue a signal they received, and in there, they find Winged Pikmin. They manage to rescue Louie, who was captured by the Scornet Maestro, only to have him land the Drake at the Garden of Hope and steal all their juice and Charlie's rubber ducky the very next day. The trio chases the thief, and along the way, find Blue Pikmin through a path that Louie managed to open with unknown explosives. Meanwhile, Louie starts recording his log but is attacked by the Quaggled Mireclops, and the creature presumably crushed the Hocotate ship into the ground at that moment. The trio eventually discover and defeat the Quaggled Mireclops, with the Hocotate ship totaled just outside the bounds of the arena, and take Louie back with them, now tying him up. Louie reveals the location of Olimar, and the explorers set out to rescue him at the Formidable Oak. The final fight happens against the Plasm Wraith, and afterwards, Olimar returns the cosmic-drive key, and the whole cast leaves the planet.
There are four endings to Pikmin 3 (and a game over state), depending on how much fruit the player obtains and if they ran out of juice or not, as explained here. At this point, none of the endings have been confirmed or denied to be canon, but due to Louie not being left behind on the planet in Olimar's Comeback, it can be assumed that the Koppaites did not collect all 66 fruits. The Koppaites couldn't have starved to death either, because if they did, the events in Olimar's Comeback couldn't occur.
Some undetermined time after the events of Pikmin 3, Captain Olimar is flying through space on his new ship, the S.S. Dolphin II, and comes across a field of asteroids. He tries to dodge them, but fails and crash-lands on an unknown planet with Pikmin and old enemies returning in it, hinting that it just might be PNF-404 again. However, its geography is completely different than the confirmed PNF-404 in Pikmin 3. The S.S. Dolphin II even calls it an "unknown planet", making it harder to believe that this is PNF-404 again. To get his ship back in working condition, he has to recover some treasures found throughout the land, so that the S.S. Dolphin II can extract their Sparklium to help power the rocket. For this, he makes his way through eight sectors worth of areas, as he re-discovers Red Pikmin, Yellow Pikmin, Blue Pikmin, Rock Pikmin, and Winged Pikmin. (The S.S. Dolphin II recognizes the Pikmin types first discovered in Pikmin 3, which is why Hey! Pikmin is known to come after it.) At some point in this adventure, he realizes that the ship lost an important piece, the Sparklium Converter. Through some effort, him and the ship figure out that the piece lies in one final sector, The Final Stretch. There, he comes face to face with the Berserk Leech Hydroe, and using the help of some Pikmin, manages to kill the creature, expose the parasitic Leech Hydroe, and recover the missing ship part. With the S.S. Dolphin II all set, Olimar gives the Pikmin one final goodbye, lifts off, and heads home safely.