In Real Life, there are blondes, brunettes, and redheads. However, in fiction there are also varying other colors. This case concerns people (girls) with blue hair.
While blondes are foolish or innocent and redheads tend to be aggressive and evil, blue hair depicts a person being either shy or nervous, or even both. Either way, blue hair is very common in fiction, particularly in anime, and if the character has special powers, they are usually associated with water/ice. Because of this, they are often paired with, or contrasted with, a redhead or someone with fire powers or a very strong and passionate personality.
Interestingly, these people also tend to be the most rational or intelligent in the group, perhaps because being socially timid is associated with bookworms. Sometimes, they seem very aloof and stoic, tending not to make any friends of their own. If they are, they are usually revealed as having a kind, friendly nature. In this way, they are the direct opposite of a Fiery Redhead. A Red Oni, Blue Oni pairing can be made with them by making the redhead brash, strong, and passionate, and the blue one calm, quiet, and down-to-earth.
A Sub Trope of You Gotta Have Blue Hair.
Compare True Blue Femininity.
See also: Rei Ayanami Expy
Examples
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Anime and Manga
Ami Mizuno from Sailor Moon is probably the best known example of this trope. She meets many of the trope's key traits. Upon her introduction, she's the Aloof Genius girl rumored to have an IQ of 300 (and is, in fact, at the top of the Rankings in exams for the entire country). Upon actually revealing her character, it's also revealed she's not aloof, just shy, and because she's so smart, other people stay away from her instead of the other way around. The live-action has her come out of her shell by being befriended by Usagi and the others as a plot point. In the manga and anime, her being a sort of outcast within the school is never mentioned again after she joins the team. The fact that she has powers over water is just icing on the cake. She's also sort of paired up with the fiery (in more ways than one) Rei due to the fact that Rei is the 3rd member to join the team and the two are Usagi's only reliable allies until Jupiter joins the team about 10 episodes later.
Ami's introversion was actually mentioned several times in the anime.
R season: first, in Bertier's Heel Face Turn episode, the sponsor of a chess tournament speaks to Ami and notes how she used to be alone all the time, but now has made so many friends. Later, a Monster of the Week exploits Ami's secret insecurities to first frame her for cheating at exams (something that's serious business for her since she's the smartest girl in Japan), then try mind raping and brainwashing her into attacking her teammates. Finally, the R movie has her recalling how other kids used to trash talk her behind her back, thinking she was an Insufferable Genius - until Usagi came along and forced her out of her shell.
In S, Ami is greatly upset at the prospect of being seen only as The Smart Guy of the group and needs Mamoru, Michiru, and Usagi's support to try to dispel it...and she becomes the target of the Monster of the Week, which is after Ami's Pure Heart Crystal. In a Tear Jerker scene, when the monster mocks Ami's loneliness, Usagi stands up for her and tearfully declares how important Ami is for her.
In Stars, during her and Haruka's team-up, Ami remembers how, as a little girl, she wanted to play basketball, but the girls didn't dare to ask her join the team since she had too much to do, leaving her alone and sad. In a subversion, Ami later recalls how she became The Strategist of the team, which lets her find the Heroic Resolve to deliver the strategy that lets her and Haruka/Uranus win the fight.
Averted with Smug Snake Cyprine from the S season (who still pretended to be one) and with Palla Palla from Super S, who was a very childish Genius Ditz.
Although Lena's hair is actually green and Sara's is actually light purple, they both fit this trope as they are usually gentle and quiet-natured.
Yuki, plays this trope very straight in the movie Disappearance of Haruhi Suzumiya. Her normal personality is more debatable. Though seemingly an Emotionless Girl, she has started showing some signs of emotion, including social awkwardness. Although some people claim her hair is a pale gray, it can also be seen as pale blue.
In comparison, Asakura Ryoko has the hair and eyes, but her personality does not fit any of the traits above. Given that she, like Yuki, is an Artificial Human, perhaps this was an intentional contrast?
While Kozue Kaoru from Revolutionary Girl Utena does not fit this trope, her twin brother, Miki, is a somewhat shy blue-haired boy.
Aria from Sister Princess is probably the most shy of all her sisters.
Akira Sakura from Naru Taru is about as shy as this trope can get, to the point of suicidal Deconstruction. It turns out that she is shy and nervous because of sexual abuse at the hands of her father combined with a crippling social phobia.
Saya from Peacemaker Kurogane, though her being shy might also have something to do with the fact that she's mute and can't say anything, even if she wanted to.
Due to a Dyejob, this is inverted with Yue Ayase in Mahou Sensei Negima!. Starting out in the manga, she has blue hair with a cynical personality obsessed with philosophy, but eventually moves farther towards shy once she begins getting closer to Negi and her hair is changed to purple.
Nodoka Miyazaki in Negima!? gets blue hair (as opposed to the other series where she is a literal Shrinking Violet) and is really shy, a bookworm, and thinks with her head.
Aoi Sakuraba from Ai Yori Aoshi, appropriately enough.
This is in contrast to her fiery guardian, Miyabi, who has purple/mauve hair.
Chrome Dokuro from Katekyo Hitman Reborn!. Though she shares her body with a man who is more psycho than shy...
Brought up in the company of adults ever since he was young, Touya Akira from Hikaru no Go tends to be somewhat awkward and shy around peers his own age. Although his hair is green in the anime adaptation, the manga colouration tends toward a darkbluetint.
Hiwatari Satoshi from D.N.Angel, another male example.
In Lucky Star, Konata's mother, Kanata, fits this trope, in contrast with her daughter, who does not (due to her father's influence).
Fairy Tail: Levy and Juvia both have blue hair. Levy is the smart and friendly type and Juvia has water powers, but also seems to be shy at times, at least around Gray.
Beginner from Mon Colle Knights has the blue hair and every opposite personality trait: extroverted, cheery, overly-relaxed in crisis situations, and the least intelligent member of the recurring cast. She can employ three out of the four cardinal elements, water being the exception.
In The Incredibles, Violet is the only one in her family with Shiny Midnight Black hair with plenty of blue highlights, and she's also the only one who is shy.
Touhou has a number of blue/indigo-haired characters, including Cirno and Remilia Scarlet, but the real example of this trope is the little blue-haired kappa Nitori Kawashiro, a Gadgeteer Genius who wants to be friends with humans, but is incredibly shy around them.
Subverted by both Florina and Farina in Fire Emblem. Farina is blue haired, but is an outspoken Gold Digger. Florina is violet haired, but fits the shy Shrinking Violet part.
Played a little straighter with a male: Celice from Fire Emblem 4 is quite the badass fighter, but is also extremely humble as a person and kinda scared of the prospect of being The Chosen One at the beginning.
Fuuka Yamagishi in Persona 3. Hers is more of a teal colour, though.
Despite her hair color bordering on being black, Naoto Shirogane of Persona 4 is this as well, albeit very covertly. The Moe factor of her shyness combined with the female vote was enough to earn her the winning spot in the school's beauty pageant, despite the fact that she ditched right before the swimsuit portion!
Pieda in Baten Kaitos Origins is an example of the "smart and friendly" variant, thus fitting this trope perfectly despite not really being that shy, except, arguably, by comparison to her Nakama.
Flora (or Nera in the DS remake) from Dragon Quest V is this.
Another subversion comes from Need for Speed : Carbon. Yumi from Bushido is blue-haired, yet has a cheery personality.
Harvest Moon games are pretty much guaranteed to have one of these, especially "classic" ones.
Visual Novels
Issei Ryudo in Fate/stay night is a male example. He's blue-haired, the most rational of the normal characters, and while almost all of his appearances are with his best friend, Shirou Emiya, he's said to be very shy.
Sakura Matou is a better example; her hair is purple, but sometimes looks blue.
Tedd Verres in El Goonish Shive is a perfect male version of this, although it's purple hair instead of blue. He was especially shy during his younger years, though he has opened up somewhat since then. He is the smartest of the group and is constantly inventing or experimenting on stuff. And, for bonus points, he frequently transforms himself into a girl for fun.
Emily McArthur in Misfile is this to a small degree. She has blue hair and is very intelligent, having already been accepted to Harvard before a year of her life was erased. However, she is only a little shy and it's only a small facet of her personality.
Mecha Maid from Spinnerette, while outgoing in her superhero guise, is extremely reserved outside of it. It doesn't help that she is physically incapable of being very expressive without her suit. She is a genius researcher and inventor, and her superhero wig is purple.
Kimiko Ross in Dresden Codak fits this trope to a T. She is easily one of the smartest people in an already highly advanced world, and is extremely logic-driven. She is constantly inventing crazy advanced technology, and even created several advanced prostheses for herself after getting half her body blown up. On top of that, she is very socially handicapped when it comes to new relationships, acting very clumsy and shy around boys she is interested in. And her hair is bluish black.
Western Animation
Marge Simpson, most notably during her college days.
