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.
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, like calling the Yellow Spectralid "Yellow Spectralids" over a likely typo in the lock-on name, 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 traveling through space, the S.S. Dolphin hits a meteor, which sends it plummeting to the surface of PNF-404, its parts scattering about. While on the planet, Captain Olimar discovers Red, Yellow and Blue Pikmin, in that order, and manages to retrieve all of his missing ship parts, starting with the Main Engine, and ending with the Secret Safe.
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 only be assumed to be the Secret Safe.
When Olimar returns to Hocotate, he finds that his company had to undergo a debt to repay the loss of a cargo of golden pikpik carrots. These carrots were actually eaten by Louie, as revealed in a cutscene that is unlocked with all levels being perfected in Challenge Mode. They land on the planet using the Hocotate ship, and while there, Olimar rediscovered Red Pikmin, collects the Courage Reactor, discovers Purple and White Pikmin, and rediscovers Yellow and Blue Pikmin, in that order. Eventually, him and Louie repay the debt and return to Hocotate, but during the trip, Louie gets lost behind. Olimar returns with the President, and both recover Louie from the Titan Dweevil.
Some time after this, Olimar and Louie return to the planet to collect more treasure. Olimar's expedition logs for this journey reveal that Hocotate Freight's new business venture failed miserably and it has been put in debt again. While they were exploring the Distant Tundra, Koppai sends three explorers to PNF-404 in search for food. On their way, the S.S. Drake ejects them and splits them 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, and encounters Red Pikmin and the Drake. He then learns that the Koppaites cannot return to their home planet without the cosmic drive key, which went missing during the landing. Somewhere along the way, Olimar finds Charlie's impact site and leaves the Anti-Electrifier with a note, due to the area having "many electrical contraptions". Sometime after, Olimar finds the cosmic drive key for the S.S. Drake, which he keeps as a souvenir for his son.
Afterwards, Alph makes his way to the Garden of Hope, where he gets Rock Pikmin and reunites with Brittany. After defeating the Armored Mawdad, as the two make their way to the Distant Tundra, Brittany gets knocked off the ship and lands in a cave where she discovers Yellow Pikmin. The Hocotatians eventually make their way to the Formidable Oak, where Louie turns back and Olimar gets captured by the Plasm Wraith after mistaking it for gold and leaving behind his 6th journal entry. The Plasm Wraith repeatedly knocks him unconcious, since his spacesuit puts him in forced-sleep. He still manages to write his last three logs during this time. Somehow, during the escape, Louie lands in the Twilight River while the ship itself crash-lands in the Quaggled Mireclops' arena. The two Koppaites reunite once more, take down the Vehemoth Phosbat and rescue Charlie. They then head off to the 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 fruit and treasure 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. While they are at it, Louie starts recording his log but is attacked by the Quaggled Mireclops and the Hocotate ship is presumably destroyed at that moment. They eventually face 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 Captain Olimar, and the explorers set out to rescue him on 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 three endings to Pikmin 3, depending on how much fruit the player obtains. If they don't bring back enough fruit fast enough, they will run out of juice and the Koppaites will presumably starve to death. If they left some pieces of fruit behind, the narrator will state that it is unclear if Koppai will prosper, during the epilogue. But if the player got them all, the announcer will proclaim a bright future for the planet. At this point, none of the three endings have been confirmed or denied to be canon. It doesn't help that the Koppaites aren't mentioned once by Olimar in Hey! Pikmin. It can still be assumed that one of the good endings are canonical, because if the Koppaites died, Olimar would still be trapped with the Plasm Wraith, and Louie with the Scornet Maestro.
Some undetermined time after the events of Pikmin 3, Captain Olimar is flying through space on his new ship, the S.S. Dolphin II (likely since the Hocotate ship was destroyed), 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. 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.