Black Mirror: Yorkie, one of the two protagonists in "San Junipero", is a painfully shy and quiet young woman. Justified - being comatose for the past 40 years doesn't give you many chances for social interaction with other people.
One episode had a girl who acted this way; nobody in the school noticed her, or for that matter even knew she existed. Through a combination of quantum physics Techno Babble and the nature of the Hellmouth, she became invisible and snapped, taking revenge on the popular girls. The end of the episode revealed that she apparently wasn't the first girl this had happened to.
Tara also fits this trope, especially in her early appearances (in season 4 and early season 5). Kill the Cutie She gets killed, though.
Willow began the show as a painfully shy and innocent Shrinking Violet, but as her self-confidence and magical abilities improved, she evolved into more of a live-action Cute Witch. Her biggest insecurity was that she still remembered her stammering pushover phase and based too much of her self-esteem on magic (complete with a temporary transformation into a Dark Magical Girl).
Game of Thrones: Melara Hetherspoon is very deferential to Cersei and is afraid of Tywin. Wisely so.
Keith Dudemeister from Scrubs, at least in his debut episode. "My Intern's Eyes" is mostly shown from his perspective (hence the title), and he spends the bulk of the episode trying and failing to work up the courage to say something to his superior, JD. Later episodes alter his characterization into a more confident Ace, however.
Young Ned from Pushing Daisies. His shyness, albeit to a lesser degree, extends into adulthood.
Star Trek: The Next Generation: Lt. Reginald "Reg" Barclay is painfully shy, especially in his earlier appearances. In his debut episode, "Hollow Pursuits", he talks to Geordi about how difficult it is for him.
Barclay: I am the guy who writes down things to remember to say when there's a party. And then, when he finally gets there, he winds up alone, in the corner, trying to look comfortable examining a potted plant.
Geordi: You're just shy, Barclay.
Barclay: "Just shy." Sounds like nothing serious, doesn't it? You can't know.