In the novel Speak, the main character goes through almost the entire school year trying to make it seems like she doesn't exist, because she called the cops at a party over the summer and her old friends and many people she doesn't even know hate her, even though her reason was that she was raped.
Lirael in the Old Kingdom series. A Second Assistant Librarian who, with borderline Wangst bemoans her lack of the Sight, which prevents her from being a Mad Oracle like the rest of the Clayr. Admittedly, it's not like the rest of the Clayr do anything to make her feel loved in the slightest. She gets... better.
Neville Longbottom from the Harry Potter series was this trope since the first time Harry saw him. He also Took a Level in Badass. Ginny Weasley plays with this. It's stated by the Weasleys that Ginny acts as a Shrinking Violet when around Harry, but is more or less normal when not in his surroundings. When we first meet her until about the third or fourth book, she has become friends with people Hermione and Luna (to whom she is the Only Friend for a while) is a lot more outspoken - which helps her to actually catch his attention, sorta.
Elizabeth "Beth" March of Little Women finds it very difficult, even painful, to talk to people outside her immediate family, and stops going to school out of shyness. She gets... a little better, but not too much. And then, she becomes an Ill Girl and dies. Sniff.
"Mother" in the Phule's Company series by Robert Asprin. Nearly the only time she speaks at a normal volume is over the communication network (she's also been a radio DJ). Talking to people in the same room is nearly impossible for her, except under serious emotional stress. Subverted in the sense that "Mother" is revealed to actually have an extremely confident and outgoing personality - she just has a neurological tic that renders her unable to talk if she can hear the sound of her own voice, which is why she's only chatty with her headphones on. (The woman once did a nude photo shoot, fer gossake.)
"How did you get Mother to go along with it?"
"Go along with it? It was her idea!"
Little Miss Shy from the Mr. Men and Little Misses Books (and also in the 80's and 90's TV series.)
Hal in Havemercy is a rare male representative of this trope.
Christine in Phantom by Susan Kay describes herself once as a shrinking violet, another time as a "wilting marigold," and again as a shrinking mouse.
Axel from The Princess 99 is shy, especially around boys but this is because she's insecure. This changes the longer she hangs around Maree-Celee and Skye, the embodiment of a loud-mouthed woman. An adult example would be Prof. Colette, who barely speaks above a whisper but don't piss her off.
Matthew Cuthbert from Anne of Green Gables. He's an incredibly shy, older gentleman who gets unbearably nervous whenever talking to women or children (or even other men, sometimes). The only women he is comfortable talking with are his sister Marilla and their neighbor and friend Mrs. Rachel Lynde, and Anne is the only child he can talk to. It's implied that he never had any romance in his life due to this. Deep down, he's one of the biggest softies in the story. But he certainly has it bad - one notable scene includes him going to the store to buy Anne a pretty dress for Christmas. Unfortunately for him, the clerk is a woman, and he's shy to the point where he stammers and stutters that he wants to buy a... garden rake, and... hayseed...in the middle of winter. He got flustered to the point where he bought 20 pounds of brown sugar. Anne once asks him if he's ever gone courting, and the author states that he'd never thought of such a thing in his life.
Maybeth in The Tillerman Family Series, to the point where in the first book she was mistaken for retarded partially because of her shyness.
In Dean Koontz's Watchers, Nora is somewhere between this and a Fragile Flower for much of the novel thanks to the emotional abuse she suffered most of her life courtesy of her aunt Violet. She later grows out of it when Travis and Einstein save her from Art Streck.
Ruth in Someone Else's War may be the most tragic case of this trope. All the more moving when she improves.
P. G. Wodehouse's character Mike Jackson, who features most notably in the Psmith series. While he's a kindhearted, empathetic boy who would do anything for A Friend in Need, he tends to come off as gruff or sullen due to embarassment. He also hates calling attention to himself, making him a good foil for talkative Attention Whore Psmith.
Taylor, the protagonist of Worm, began the story this way thanks to a year-and-a-half bullying campaign, but Grew a Spine after she began kicking ass as the supervillain Skitter.
Cuff, of the Chicago Wards, is a more enduring example. While she's capable of kicking ass with the rest of them using her Extra-ore-dinary metal-manipulation powers, she's normally shy and avoids conflict.
A somewhat darker example in Hector, the protagonist of The Zombie Knight. Not only is he immensely shy and frequently struggling with his own words, but also killed himself out of loneliness and depression. Obtaining undead superpowers does not (as of yet) appear to have changed this. Upon rescuing someone from being tortured and killed, he had this to say:
"Sorry. I’d untie you, but... you should probably stay and explain... uh, to the police... about what he tried to do to you. Otherwise, he could... you know... get away with it... and... yeah...”
"Oh! But, uh... don’t worry! The police will be here any minute. And he’s unconscious now. And I tied him up just in case. So... uh... y-you’re safe, now. And I-I should, I should go..."
In Protector of the Small, Gower's niece Lalasa is painfully timid owing to a lifetime of abuse, the death of her family, and being harassed by the men in the palace (who either think that her shyness is a sign of flirting or just see her as an appealing victim). After a shaky start, Kel befriends her and teaches her self-defense.
Beka Cooper, the protagonist of Provost's Dog, is painfully shy and flames out in front of the gods and everyone when she has to testify in court. She's able to put it aside when she's doing the actual work of chasing and questioning, though, and by the second book it's much less of a problem.
Literature/The Murderbot Diaries: Yes, Murderbot has guns built into its arms. No, it does not want to make eye contact with you during a conversation. At one point, it is so overwhelmed by all the attention being focused on it that it goes and stands in the corner.
The protagonist Lee Fiora in the novel Prep, who notes that this wasn't always the case and she was a normal, bright kid back in her hometown in Indiana, but at Ault Academy she is overwhelmed by her affluent, connected peers and becomes a Shrinking Violet to cope with the complex social politics of the school.