Karen, the girl who gives Masayuki a love letter in A Profile, is so shy and socially misfit that when giving a love letter (something that Masayuki's friends laugh at) she forgets to add her name or meet him for several days despite the fact that he responds rather positively.
Ron Delite of the third game, to the point that his dialogue often trails off into inaudibility (represented by the text fading into the background). This is rather ironic because his alter ego is the flamboyant thief Mask☆DeMasque.
Also, Ben Woodman, the ventriloquist from the second game. Ben, in fact, is so bad about this that he completely lacks the capacity to function among other people without the aid of his (rather abusive) dummy, Trilo Quist.
Sakura Matou from Fate/stay night, due to the horrendous mental and physical abuse that she suffers from her brother and Grandfather.
Hanako Ikezawa of Katawa Shoujo most definitely counts. The first time Hisao tries to talk to her, she actually runs away.
Hanako deconstructs this, showing in detail one of the kinds of traumatic events that would lead a person to be like this and how difficult her life is because of it. By the time the player learns all she has been through, the tears won't stop coming. Even more so, she's well-aware of how harmful being a Shrinking Violet and if Hisao and Lilly don't stop trying to coddle her... she will explode and call Hisao out on his White Knighting.
Shannon from Umineko: When They Cry. However, she's later shown to be more confident and determined when it counts.
Rin from Little Busters! is an interesting example - while she's definitely very shy and fearful when it comes to people she doesn't know, her personality around people she is close with is more like that of a TomboyishTsundere.
Touko Fukawa is a more unique example. Instead of this trope being played for cuteness, Fukawa is instead a very unpleasant Jerkass and tends to be rather depressing and moody.
In Super Dangan Ronpa 2, Kazuichi Soudaused to be this back in middle school, due to being badly bullied. They've been trying to grow out of this, changing their image to what they believe will make them more popular and help them make new friends at Hope's Peak.
Taken to the extreme with Mikan Tsumiki, who always seems to be on the verge of tears when anyone talks to her. When she's outed as the murderer in Chapter 3's trial, she stops being this.
Shiraki Aeka from Yume Miru Kusuri is the most obvious example in the game, but the seeming Manic Pixie Dream Girl Cat Sidhe Nekoko doubles as one once her "true self" is revealed.