5, from 9 is yet another male example (despite being a ragdoll, yes, he is male). Shy, skittish, hardly ever makes eye contact with those "above" him...The fact that he's also The Woobie help this.
In the Disney adaption of Alice in Wonderland, when Alice stumbles on to a talking garden, they promised her that they would sing a song to her. All the flowers wanted to sing about themselves. The violets wanted to sing about themselves, and when they brought up the suggestion, they were quiet and they slowly backed up in the shade below the other flowers.
The protagonist in the movie Coyote Ugly is one of these. As a bonus, her name is actually Violet.
Todd from Dead Poets Society starts out so shy he can barely speak in front of others. He later gains confidence thanks to Neil and Keating.
Need Shrinking Violet personified? Well, look no further than the appropriately-named Violet Parr from The Incredibles, pictured above. Not only is she incredibly shy, but she also has the hair, the mumbles, and a desire to be just another girl, and she can't even look the school heartthrob, Tony Rydiger, in the eye. Her family are superheroes in hiding, and her powers are invisibility and forcefields—Word Of God is that these are symbolic of her personality, respectively being her wish to hide from everyone else and her need for insulation from the rest of the world. Needless to say, she embraces her abnormalities, gets an Adrenaline Makeover, and puts her hair back in the process of helping her family save the world.
And to top it all off, by the end of the movie, it's Tony who can't look Violet in the eye, instead of the reverse. Think about it.
In another Pixar film, Inside Out, this is played with by Fear: despite being male (albeit representing the emotions of a girl) and a bit more outspoken in showing how he's afraid, he's still repressed temerous, and his skin is purple.
Prince Albert (later, King George VI) in The King's Speech has a painful stammer, which has left him deathly afraid of public speaking and large crowds in general. The crux of the film features him attempting to rectify this in the face of the looming threat of World War II.
The title character of May is a similar example, minus the telekinesis. Poor May's only comfortable social interactions are with the doll she calls her best friend. She's so shy that she can barely talk in the presence of other people at all, even when they're clearly interested in getting to know her. Although once she's decided to kill them all, she becomes much more confident.
Funnily enough the actress that portrays May (Angela Bettis) also played Carrie in the NBC TV remake in 2002.
Mishima A Life In Four Chapters: Both Kimitake and Mizoguchi have stammers and are painfully shy and awkward. By the time they get over it real and fictional Japan are in for a shock or two.
Not quite on Fluttershy levels, but the human Twilight is quite timid. Even when the rest of the students of Crystal Prep are cheering, she's timidly off to the side, looking away.
Sunset Shimmer meanwhile has completely regained her confidence, even briefly displaying the temper she had from the first film.
My Little Pony: Equestria Girls Rainbow Rocks: Sunset Shimmer's normally brash, confident, and collected, but she was certainly this in Rainbow Rocks; the events of the first film destroyed her worldview, and left the whole school still hating her but no longer afraid of her. As a result she has no friends (or that we see, a social life at all) outside the Humane Five, is uncomfortable being the center of attention, and watches the Rainbooms fall apart without interjecting because she feels it isn't her place to get involved. It's telling that when she shrinks down, she gets slightly knock-kneed and starts rubbing her arm, just like Fluttershy in the last film. Her Character Development has her reverse her descent and get over her fears, stepping into the spotlight in a more positive way than before.
Cadet Hooks from the first Police Academy movie spends almost the entire film unable to look other characters in the eye and barely speaking above a quiet whisper, until very near the end when arresting a suspect when she screams "DON'T MOVE, DIRTBAG!". She continues to do that in every other Police Academy movie she's in. (Really, if someone that quiet started yelling like that and had a gun, wouldn't you feel like doing what they said?)
Barry from Punch-Drunk Love is another male example, though he deals with his shyness and frustration through aggressiveness.
Mui, the female lead of Shaolin Soccer. Hair in the face, mumbling, acne, withdrawn, eventually pulling out of life in public to become a nun. Until the final showdown.
In Suffragette Maud starts out as this. Ironically, her co-worker who is actually named Violet is much more outspoken, and invites Maud to a suffragist meeting. It is Violet who was to read a testimony of her experiences in the laundry where they both work, but Violet's husband beats her up so that it is decided she cannot speak in front of MPs (Violet would, but others think she won't be taken seriously with a black eye and all that), and Maud is persuaded to take her place. After that, Maud is still hesitant, but after the police arrests her for the first time, there's no turning back, and Maud embraces her new role as freedom fighter. Her boss at the laundry is very surprised when she pushes a hot iron on his hand after he taunts her, again, with the fact that he rapes the underage laundresses with impunity, something he also did to Maud when she was younger.