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. 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.
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?
Miki Kaoru from Revolutionary Girl Utena is a male example, being a gender-switched Expy of Ami Mizuno down to the same voice actress. Interestingly enough, his twin sister Kozue does not fit this trope.
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.
Due to an Adaptation Dye-Job, 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.
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.
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.
Yoshino from Date A Live, in addition to being An Ice Person, is extremely shy and soft-spoken. She deals with this by communicating through her hand puppet 'Yoshinon' whenever the situation calls for a more extroverted approach.
The White Magician Girl Ninian, however, plays this almost perfectly straight. Her hair is more cyan than properly blue, but she is very humble and kind and has quite the problems interacting with people.
Played a little straighter with a male: Seliph from Genealogy of the Holy War 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.
Boy!Morgan mayfit in if he's fathered by either Chrom, Virion or Priam, though.
If a blue-haired Avatar has daughters, only Noire will be a straightforward example. Though Yarne could potentially be a Rare Male Example, even if he only has a blue streak on his fur.
Noire and Yarne might fit if either is fathered by Virion, too.
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 True Companions.
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.
Averted with Shizune Hakamichi from Katawa Shoujo, who is blunt and outspoken — despite being deafmute. Still worth noting, though, as when they're introduced, Hisao thinks she's one of these until she "opens her mouth," so to speak. The most shy girl in the cast, Hanako Ikezawa, has purple hair.
Mio from Little Busters! is a very quiet, soft-spoken girl with an emotionless personality who is almost always found sitting and reading on her own at the back of the school before Riki comes across her. He even notes at one point that, in complete contrast to him who defines himself by his Childhood Friends, she seems to long to be truly alone, and her presence is so low that people often seem to forget she even exists. Her route provides an explanation for all of this.
Araceli of Hazard's Wake is very much this, though the shyness probably comes from being locked in a tower for most of her life.
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 some degree. She has blue hair and is very intelligent, having already been accepted to Harvard before two years of her life were erased. She is only a little shy and it's not a large facet of her personality, but she definitely pairs well with Ash.
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.