Sonic the Hedgehog has several odd-colored animals. Sonic has blue spines/quills, Amy Rose has pink hair/quills, Big and Blaze the Cat are purple, Scourge was formerly blue, now GREEN hair, and almost every single echidna having red hair in the Archie Comics, the list goes on. Averted with human characters, who have natural hair colors, even in their more cartoony depictions. However, the GUN Commander's hair (which is supposed to be white) was bizarrely colored purple in Sonic Chronicles.
In Mega Man Battle Network, Chaud has two-toned white hair and black sides, Mayl has purple hair, and Dex has a fin on his head. Maddy has outrageous bright pink (with a giant poofy style, even), Shuuko has a pleasant shade of indigo, and Raika has light aqua-green hair.
Battle Network's sequel series, Star Force, which is filled with insane hair styles. Sonia's hair is PURPLE! Pat's hair is green due to Theme Naming.
Picking on Misora's relatively normal (color notwithstanding) hair when Twin-Drill Luna◊-iinchou is right over there?
The third game has Eos and Queen, who have matching shades of actual blue hair, and Heartless, who sports a pink 'do.
And Mega Man ZX is an even worse offender. Grey has...grey hair. Ashe has blue hair. Other main characters have strange hair colours and styles...The strangest of them all has to be Prometheus and Pandora. Prometheus' hair is blue, and Pandora's hair is green, and they look like capes until you notice the one scene in Advent where they don't have their helmets on. But Prometheus can kill people with his hair. Albert has two hair colors in a different way than other people. He has teal hair in his Sage Trinity body, but his "real body" has freaking magenta.
ZX aside, the main universe is actually pretty sensible about this. The original Mega Man did have blue hair at one point, but he usually switches between black and brown. The Zero series doesn't even have one exception. In Legends, we have the purple haired Mega Man Juno, who is obviously inhuman, and the mysterious Yuna and Sera and their servants, synthetic lifeforms of indeterminate type whose humanoid forms resemble black women with light green hair.
The X-series is a little more varied. From Command Mission, we have Nana, who has pink hair with a single white bang, Scarface, who personifies this trope with light-blue spiky long hair, and the seafoam green-haired Marino. Dynamo from X5 and X6, who personifies this trope with an aqua blue hair. Lumine from X8, who has purple hair that is styled in a mix between whatever Tron from Legends has going on plus an emo hair fringe, and also from X8 is Layer with purple hair AND Pallete, who has blonde hair with pink stripes in an...unexplainable style◊. Axl from X7/X8/CM has pretty normal hair normally, but when he uses his "white mode" in X8, it turns purple (to reflect an implied connection to Lumine). And amongst other modes is any of Zero's other forms who have a lighter shade of blonde to them. The unnamed female Navigator from Maverick Hunter X, who has pink hair.
Advance Wars: Days of Ruin has, despite its generally more realistic tone, a blue-haired and several teal-haired characters. A redhead too, but at least that's a possible color in real life, if rare. Most characters stay in the realistic range, but it's still a third of the playable cast. All of these characters are "clones" of the same character, however that works. (We're talking multiple genders here, people.) Not that that really explains anything, but still...
Gage's blue hair is still completely unaccounted for.
Fire Emblem has lots and lots of strange hair colours to the point that Leif (the main character in Thracia 776) having brown hair is extraordinary, this is somewhat lampshaded in the Path of Radiance and Radiant Dawn, where Ike and Micaiah are always identified by their hair colour (Blue and Silver respectively, Micaiah even has the title "Silver Haired Maiden"). In fact, Fire Emblem characters can often tell their own families by hair color. In the Elibe saga, red-haired Roy and blue-haired Lilina inherited the hair colors of their respective fathers (Eliwood and Hector), and Nils and Ninian from the prequel have the same pale green hair. Similarly, twins Ephraim and Eirika from The Sacred Stones both share a light teal with their father. Let's not forget Marth and his sister Elice from Shadow Dragon and Mystery of the Emblem. Examples of characters sharing colors with their parents and siblings go on like this for a while and is even a game play mechanic in Fire Emblem Awakening where second generation characters always inherit their father's hair color with one or two exceptions where they get the mother's color. Truth be told, the Fire Emblem series tend to alternate between having a traditional blue-haired protagonist in one game and one with a different hair color in the next. Marth (from Shadow Dragon and Mystery of the Emblem), Sigurd and Seliph (from Genealogy of Holy War), Hector (from The Sword of Flame), Ike (from Path of Radiance), and Chrom (from Awakening) all have blue hair, while Alm and Celica (from Gaiden), Leif (Thracia 776), Roy (from The Binding Blade), Lyn and Eliwood (from The Sword of Flame), Erika and Ephraim (from The Sacred Stones), and Micaiah (from Radiant Dawn) are all exceptions.
Inverted with a deadpan kind of hilarity in Digital Devil Saga: the girl who fell from the sky is instantly recognizable and keeps the characters in a kind of awe with her bizarre black hair and brown eyes. Fluorescent-red-haired Heat, purple-haired Argilla, and green-haired Gale simply can't understand how a human could have such a strange hair colour.
Tales of Symphonia looks to avert this for 2/3 of the first disk, with humans having only realistic hair shades and only Elfs (and Half-Elfs) having strange hair colors (such as teal), but then you go a parallel world and find people with lots of strange hair colors such as blue and pink.
In Tales of Symphonia: Dawn of the New World, there is a skit where Tenebrae is offended by Genis' comment on his age, and Tenbrae reminds him that he has a full head of white hair. Genis responds with: "It's SILVER!!!"
Tales of games tend not to bother, really. Highlights of the series include Meredy's lavender (Eternia), several types of bright pink (Arche from Phantasia, Chelsea from Destiny, Presea from Symphonia, Hermana from Innocence and Cheria from Graces), and a smattering of blues and greens for good measure.
Hearts averts this (Mechanoids and aliens excluded), to the point where the Mysterious Waif and Big Bad are explicitly identified by hair color; myths describe an "emerald-haired princess" and a "devil of blood-red hair". Well, mostly. The Quirky Miniboss Squad has hot pink and teal.
Vesperia colors Yuri's hair purple, Estelle's pink, and Judith's blue.
The party in  doesn't fall under this rule, but it does include pink-haired Arietta, whitish-haired Dist, and Ion, Sync, and Florian, who all have green hair. The Kimlascan royal family does sport all red hair, though, in shades varying from dark (Duke Fabre) to the fiery orange Luke sports.
Even though the Ace Attorney series takes place in a fairly realistic universe, no one seems to feel the need to comment on the hair colors of Franziska, April, Vera, Redd, or Lisa Basil (metallic blue, pink, dark blue, purple, and electric blue, respectively). While Redd and April could've dyed theirs, and Lisa's could just be part of her gimmick, Franziska's and Vera's hair really has no explanation. And that's not even getting into some hair ''styles'' that seem to completely defy the laws of physics.
A large majority of Disgaea characters, demon or not, have absurd hair colors ranging from blue to white to neon pink.
While Link's hair has historically fluctuated between red, brown and blond in his various appearances, his hair was inexplicably pink in The Legend of Zelda: A Link to the Past. It also justifies why Link becomes a pink-furred rabbit in the Dark World.
In The Legend of Zelda: Ocarina of Time, Link's childhood friend, Saria, has vibrant green hair. She's the forest sage as well, which may explain her unique hair colour in relation to the usually brown haired kokiri.
The teenager who runs Bombchu Bowling Alley in Ocarina of Time and the Treasure Chest shop in The Legend of Zelda: Majora's Mask has neon blue hair and wears a hot pink shirt. Ironic in Ocarina of Time, where she runs a business based on big moving neon targets.
Falling somewhere between all examples is Ritz from Final Fantasy Tactics Advance, a girl who has crimson hair, even in the "real" world. It's a dye-job, as her hair appears to be albino (pale lavender) despite the rest of her.
In Elite Beat Agents, Agent Foxx has silver hair. Meanwhile, Cap White has pink hair...and she's a white blood cell. Also, Morris seems to have purple hair, Derek has red hair, and J's is orange.
Humans in Cave Story tend to have dark green hair (of the few we see, anyway). Supposedly, this is because the game's creator found that black hair wouldn't stand out enough against the caves' dark backgrounds. There's also Misery, who has blue hair (or green, depending on whether you're looking at her in-game sprite or her character portrait...).
The Servants in Fate/stay night don't count, but a couple of the humans have strange hair too — most obviously the Matou siblings, Sakura (purple), and Shinji (blue). You don't want to know how Sakura ended up that way...
Sakura is actually a subversion, because purple is not her natural hair colour, and the reason behind this is a big part of the plot of the Heaven's Feel route of the game.
Ciel in Tsukihime has bluish black hair, predominantly black if you look carefully. In text, meaning according to the author, she has black hair.
Persona 2 averts this. We have a character with blue hair, Eikichi. He dyes his hair every. single. morning. before school, and then washes it out before he goes home. It's not natural, but it's still pretty improbable.
Prevalent throughout the Phantasy Star series. It's generally the alien races like Newmans and Dewmans who favor odd hair colors.
Phantasy Star Online 2 deserves special mention for letting you have hair of literally any color in the spectrum, thanks to its huge amount of character customization.
Super Robot Wars franchise original characters. There's a fair amount of brown or blond haired characters, but just point at random and 7 out of 10 times, it will be someone with an unnatural hair color.
Optional for The Sims 3. You can now give your sim exotic colors, with exotic highlights. Give them a head full of rainbow if you like.
Kingdom Hearts isn't immune to this. We have the white haired Riku, all of Xenahort's variations, and, while not relevant to the plot, Sephiroth). Zexion, Saix, and Aqua all have blue hair. And last but not least, Marluxia has pink hair!
The Gria race from Final Fantasy Tactics A2 have four assortments of hair colors, depending on the class: red for Ravagers, blue for Hunters, green for Raptors, and purple for Geomancers.
Final Fantasy. The graphics of the original game don't allow for much in the way of zaniness (with the exception of the Red Mage's white hair and, in early versions, the Thief's blue hair), but Amano's original artwork and FMVs in the later remakes of the game have the Warrior/Knight character with silver/white/grey hair.
From Final Fantasy II, there's Firion, with white hair as a young man, Maria and her indigo hair, Leon and his blue hair, and Leila with either blue or violet hair.
Luneth in the DS remake of Final Fantasy III has silver-gray hair despite being a teenager. Desch has blue hair in the same remake.
Terra from Final Fantasy VI has either green or blonde hair, depending on whether you believe the sprites or artwork. Dissidia splits the difference by giving her blonde hair in the main costume and green hair in her alternate costume. Setzer's also got a headful of white/silver hair, due to (possibly) being albino. Lastly, although Amano draws him as a blond, Locke's game sprites and portraits have dull grey hair. And her overworld sprite also resembled Bulma from Dragon Ball because of the hair color.
In Final Fantasy XII, all Viera are born with white hair, though, according to the manual, some of them dye it human colors. Penelo's concept art shows that she was originally going to have pink hair rather than her current blond.
In Final Fantasy XIII, Lightning and Serah both have pink hair. Vanille has super-bright red hair, but definitely not a natural shade. Hope has the ever popular silver hair, as does NPC Yaag Rosch, though his has more of a blue tint. Lastly, NPC Yuj/Yuge has blue hair of an alarming shade.
Final Fantasy XIII-2: Added to the cast of the previous game, we have Caius Ballad, whose hair is purple, and Yeul, whose hair is blue in pre-rendered cutscenes and concept art, but appears much closer to silvery-white in-game.
Final Fantasy Tactics gives Marquis Elmdore some Sephiroth-hair, though his age (39) means that it might just be due to natural aging...well, if he's aging really, really badly. The final boss, Ultima, has silver hair, though, and so does her human vessel, Saint Ajora.
Selkies, a race in the Crystal Chronicles series, have this as one of their defining features. The only "normal" hair colors among them are red and blonde.
In Final Fantasy XI The Tarutaru, are the only playable race with the option of blue and green hair. The Mithra, Elvaan, Galka, and aforementioned Tarutaru have the option of white and grey hair. The Hume race only features natural hair colors. Outside of PC's there's Prishe, an Elvaan with lavender hair.
Final Fantasy XIV throws "realism" out the window when it comes to hair color for playable characters: No matter what race you pick, there are dozens of shades of grey, green, red, pink, blue, purple, and on and on to choose from.
While there are many characters in the Jak and Daxter universe with 'normal' hair colors such as brown, blond, and grey, many others sport shades far more exotic. Often overlaps with Multicolored Hair. Some examples: main character Jak's hair is green and yellow, Keira's is green and blue, and the sculptor's is purple.
A number of characters in the Pokémon games have oddly colored hair. Steven, for example, has white-silver hair, despite seemingly being in his early 20s. Brendan also appears to have black and white hair, though that's very much debatable.
There's also Kris, Dawn, and Lucas, all of whom appear to have blueish hair (light blue for Kris, dark for Dawn and Lucas).
N and Ghetsis have green hair. Ghetsis' seems to be going grey from age, too.
The Striation gym leaders' hair all matches their Elemental Monkey...green for Cilan and Pansage, blue for Cress and Panpour and red for Chili and Pansear.
The Fuchsia City nurse has green hair, while every other city's nurses are redheads.
Mother 3's Princess Kumatora and the Magypsies have bright pink hair.
The cast of the Touhou series of games can be handwaved as Improbable since most of them aren't human, but with a few exceptions:
Sanae Kochiya, a human who, until recently, lived in the outside world, has green hair. She does have divine blood, but the god she's descended from is blonde, so...
Marisa Kirisame, despite being a full blood Japanese, has blonde hair (or red in her first appearance). She is a witch though, and it could easily be explained away that she used a spell to change her hair color. However, in Curiosities of Lotus Asia , it showed her as having light hair a child, with no real explanation, so she could have been born with it.
Sakuya Izayoi has white/silver hair. She does have a mysterious past, but everything suggests she's human. Mostly.
Fujiwara no Mokou has white/vaguely lavender hair. She is an immortal, so this may simply be the result of aging. However, her brand of immortality includes eternal youth, so there may be another reason.
Mokou's silver hair is implied to be a result of drinking the Hourai Elixir. Kaguya, the other character who drank it, has black hair, but she's a Lunarian, who naturally have silver hair, so probably the same thing happened to her in reverse.
Keine has blue/white hair. She's a were-beast, but her were-form has a different hair colour (green), and what we know about the curse suggests that it should have an effect when it's not active.
Yorihime has purple hair. Sure, she's from the moon, but the lunarians are just displaced humans.
Rinnosuke has white hair, even though he's supposed to be fairly young, although he probably gets a pass for being youkai-human hybrid.
The characters of ORANGE_JUICE's SUGURI and sora series have varying hair colors. Examples includes:
SUGURI's titular heroine, who' has white hair.
For the first game's bosses, there's Iru, who has lime-colored hair; Nanako's hair is purple; and finally played straight with Kyoko who has long, blue hair, which matches up with her personality considering she's a calm and collected ice-user.
As for sora, it's titular heroine has peach-blonde hair with a notable touches of pink.
sora's bosses plays blue-haired girls straight, as you have Tsih, the game's blue-haired Genki Girl ice-user; and Nath, an armless mecha pilot who also has blue hair;and then finally Starbreaker, the first game's Final Boss.
In Fallout 3, you can create your character to have vastly unnatural hair colours, and all the Raiders have unnatural hair colours. One character says that her daughter 'has dyed orange hair', so it's accepted as dye-jobs, but given the general lack of surviving pre-war supplies and blasted landscape, it's likely they aren't using local plant life or commercial dyes... which might explain the insanity and violence of raiders.
Many characters have blue/green/pink hair in the later games in the Backyard Sports series.
As a general rule, most examples of this in the Breath of Fire series fit as Plausible Examples—the one that does not would be that of Ryu 1/8192 in Dragon Quarter as he starts out as a normal, actually fairly low-caste human with dark blue hair. (And yes, Word of God explicitly states this Ryu was meant to be a normal human.)
Mitadake High, being a game which gloriously bases itself on all manners of Anime stereotypes, lampshades this by having the aliases of most of the characters be their hair colour (such as "The Blue Haired Boy" or "The Long Pink Haired Girl"). In fact, the only two that aren't are "The Boy With Goggles" and "The Boy with Sunglasses" (which are other stereotypes anyway). The hair colours are: Blue, Red, Green, Orange, Purple, Brown, Black, Silver, Grey, White, and Blonde.
Grandia provides a full palette: hero Justin has vibrant red hair, childhood friend Sue's is purple, Action Girl Feena sports green while her sister Leen's is blue, Quirky Miniboss Squad Nana, Saki, and Mio are purple, red, and green respectively, and ethereal White Mage Liete has purple.
Yo-Jin-Bo has Muneshige, Bo, Kasumimaru, and one of the unnamed ninja with blue hair. Yo's aqua hair could also count.
Princess Kaguya and the March Hare from A Witchs Tale both have green hair.
In Baten Kaitos, Kalas and Sagi have blue hair, Lyude has fire-engine-red hair, and Savyna has purple hair (that's blue in the prequel for some reason). Some NPCs also have weird hair colors.
Tomba's pink hair. It was part of the American ad campaign.
A good portion of characters from Infinite Space have implausible hair colors; some characters (including The Hero) has white or gray hair, the main character's sister has green hair, and then a few others have blue hair. While this may be justified with the fact that human race had been modified by the Overlords long time ago, and Yuri and his sister are Artificial Humans, that still doesn't explain the rest with natural hair colors.
It will be easier to list the characters from Lux-Pain who have natural hair colors.
Kit Ballad of Blade Kitten has pink hair for no explicable reason.
In Jet Force Gemini, one of the main trio, Vela, has blue hair. It's possible it's natural but it's never stated. Unlike her brother Juno, she doesn't wear an armoured helmet, probably just to show it off.
In Children Of Mana, Ferrik and Tamber have orange and green hair, respectively.
In Telefang 2, the protagonist, Kyou, has blue hair.
And then there are the people of Prox, who are all Mars Adepts but have an absolute rainbow of possible hair colors, justified since the Pointy Ears and scales make it pretty clear they're not entirely human.
There's purple hair, blue/white hair, green hair, orange hair, and purple black hair in Canvas 2, but somehow, only Elis' blond hair is noteworthy.
Milked for all it's worth in the first three entries of the Tokimeki Memorial series. Virtually all impossible hair colors are used but the white one, along with realistic ones.
Becoming a growing trend in Harvest Moon games. The first game had only the pink-haired Nina (and the second, her Identical Granddaughter Popuri), and the latest installment features pink (Luna), magenta (Selena), teal (Phoebe, Harvest Goddess), lime-green (Barbara), blue (Candace, Luke in some lights), violet (Julius), AND White (Witch Princess).
Substitute hair with fur in Star Fox; Krystal is a blue vixen and Falco Lombardi is a blue pheasant. Arctic foxes have shades of bluish fur, but have a scant amount of it, and blue falcons don't exist. There are also Katt (a cat), Lucy (a hare), and Amanda (a frog), all whom are pink.
Lucca of Chrono Trigger has purple hair. Magus has blue hair in-game, although the official art has it closer to white.
The King of Fighters have several characters with blue hair, such as Leona and Elisabeth. There's also Kula, although her hair is blue only when she's fighting. Then some characters also have multi-colored hair, such as Goenitz, Alba Meira, and more.
A male and plot related example from Wild ARMS. Rudy, one of the main characters, has blue hair. The only other characters we see with odd colored hair are the interdimensional demons that are attacking the world. This is foreshadowing that Rudy is not human, and we eventually find out he is a robot made from metal the demons forged.
Ys I and II has the goddesses Feena and Rea/Lair (the latter's hair was changed to purple in IV), and The Ark of Napishtim has Olha and Isha, of the nonhuman Rehda.
Artix Entertainment games often have this trope, including Warlic, who has white hair, and Valencia, who has dark purple hair. In all of their games, including MechQuest and AdventureQuest Worlds, the player character can choose their hair color, which can lead to instances of this.
In AdventureQuest, Lady Tomo's hair is purple, and Aelthai has a bright shock of purple hair.
In Dragon Fable, Elysia and Nythera also have purple and blue hair, respectively.
In the Valis series, Yuko has blue hair, Reiko has purple hair, Valna has light blue hair, and Lena has pink hair.
In both the Baten Kaitos games, the protagonist has some shade of blue hair; Kalas' is bright, sky-blue, while Sagi's hair is closer to a shade of teal.
In Golvellius, the hero Kelesis has green hair.
In the Etrian Odyssey series, players select portraits representing their characters. While a few instances appeared in the first two games, such as a pink-pigtailed Troubadour, III opened the floodgates by introducing Palette Swaps to the mix. In IV, violet, green, and teal blue are particularly common alt-colors.
Goemon of the Ganbare Goemon series has blue hair in all but the earliest games, where he was supposed to be a redhead.
Xenoblade is actually pretty subdued in this respect. With the exception of a pink-haired Mauve Shirt near the beginning of the game, strange hair colors are mostly limited to the High Entia race.
Xenogears has an interesting one; all of Miang's incarnations have indigo or black hair.
In The Legend of Prince Valiant for the NES the eponymous prince is depicted with neon blue hair, as opposed to his traditional black "Hair-helmet". It was made by King Features and Ocean both of which are Western companies.
The cast of Neptunia have a very diverse range of hair colors; there's purple, black, white, blonde, green, light blue, pink, brown, blue, red...
Bravely Default: The majority of women in Florem, because of Petal Hue, a bright blue hair dye. Becomes plot-important when it's revealed that the dye is poisonous (which is why the women have become so shallow in recent years), and part of a multi-step plan to topple Crystal Orthodoxy in their nation.
The trope is taken in a more literal form by the aforementioned women; it is in their general opinion that one of the hallmarks of true beauty is the exotic hair colour Petal Hue offers.
The Mii avatars you can make on variousNintendoplatforms cannot have unnatural hair colors. In Tomodachi Life, however, you can obtain a hair-color spray item that allows you to give a Mii non-natural hair colors. Unfortunately, if you then give that Mii a bath, they will lose that color and their hair will revert back to its natural color.